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This document provides an overview of probability theory, including key definitions, concepts, and calculations. It discusses: 1. Definitions of probability, including the frequency and subjective concepts. It also defines basic terminology like experiments, trials, outcomes, and events. 2. Methods of calculating probability, including classical and empirical approaches. It presents the classical probability formula. 3. Common probability distributions like the binomial distribution and normal distribution. It provides examples of calculating probabilities using these distributions. 4. Additional probability concepts like independent and conditional probability, random variables, and transformations to the standardized normal distribution. 5. The importance of the normal distribution in applications like medicine, sampling, and statistical significance testing. It

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RSS Hypothessis testing

Hypothessis testing by Dr. O. Yusuf as part of the 5th Research Summer School - Jeddah at KAIMRC - WR

Continuous probability Business Statistics, Management

This document discusses different types of continuous probability distributions including uniform, normal, and exponential distributions. It provides examples of how each distribution is used and defined mathematically. The normal distribution is described as the most important for describing continuous random variables. Real-world examples of when each distribution would be used are given, such as height, test scores, and time between events. Business applications like risk evaluation, sales forecasting, and manufacturing costs are also summarized. Finally, it emphasizes that probability is involved in many aspects of daily life beyond just academics.

Psych stats Probability and Probability Distribution

The document discusses key concepts in probability, including analytic, frequentist, and subjective views of probability. It covers terms like events, independence, dependent events, mutually exclusive events, and exhaustive events. Laws of probability like the additive law and multiplicative law are explained. Examples are provided to demonstrate calculating probabilities using tables and the normal distribution. The central limit theorem and law of large numbers are introduced.

Rafeek

This document provides an introduction to probability and probability distributions. It defines probability as the likelihood of an event occurring, and discusses how probability is measured on a scale from 0 to 1. It then covers key probability concepts like experiments, common probability terminology used in medicine, the two views of probability (objective and subjective), and the four types of probability (marginal, union, joint, and conditional). The document concludes by introducing common probability distributions like binomial, Poisson, and normal distributions and providing examples of how they are used.

Fundamentals Probability 08072009

The document provides an introduction to probability theory, including definitions of key terms like trial, event, exhaustive events, favorable events, independent events, mutually exclusive events, and equally likely events. It discusses three approaches to defining probability: classical, statistical, and axiomatic. The classical approach defines probability as the ratio of favorable cases to total possible cases. The statistical approach determines probabilities based on empirical observations over many trials. The axiomatic approach uses set theory and axioms to define probability without restrictions of previous approaches.

Probability

Probability not Higher Level....This PPT is for beginners or for those who learnt or to study PROBABILITY........... :):):):):)

Probability Concepts

classical, empirical, and subjective
approaches to probability.conditional probability and joint
probability.Bayes’ theorem.

Probability

The document discusses probability and set theory. It defines probability as a quantitative measure of uncertainty or a measure of degree of belief in a statement. It states that probability is measured on a scale from 0 to 1, where 0 is impossibility and 1 is certainty. It then discusses key concepts in set theory such as sets, subsets, Venn diagrams, and operations on sets like union, intersection, difference, and complement. Finally, it discusses definitions of probability including the classical, relative frequency, and axiomatic definitions.

RSS Hypothessis testing

Hypothessis testing by Dr. O. Yusuf as part of the 5th Research Summer School - Jeddah at KAIMRC - WR

Continuous probability Business Statistics, Management

This document discusses different types of continuous probability distributions including uniform, normal, and exponential distributions. It provides examples of how each distribution is used and defined mathematically. The normal distribution is described as the most important for describing continuous random variables. Real-world examples of when each distribution would be used are given, such as height, test scores, and time between events. Business applications like risk evaluation, sales forecasting, and manufacturing costs are also summarized. Finally, it emphasizes that probability is involved in many aspects of daily life beyond just academics.

Psych stats Probability and Probability Distribution

The document discusses key concepts in probability, including analytic, frequentist, and subjective views of probability. It covers terms like events, independence, dependent events, mutually exclusive events, and exhaustive events. Laws of probability like the additive law and multiplicative law are explained. Examples are provided to demonstrate calculating probabilities using tables and the normal distribution. The central limit theorem and law of large numbers are introduced.

Rafeek

This document provides an introduction to probability and probability distributions. It defines probability as the likelihood of an event occurring, and discusses how probability is measured on a scale from 0 to 1. It then covers key probability concepts like experiments, common probability terminology used in medicine, the two views of probability (objective and subjective), and the four types of probability (marginal, union, joint, and conditional). The document concludes by introducing common probability distributions like binomial, Poisson, and normal distributions and providing examples of how they are used.

Fundamentals Probability 08072009

The document provides an introduction to probability theory, including definitions of key terms like trial, event, exhaustive events, favorable events, independent events, mutually exclusive events, and equally likely events. It discusses three approaches to defining probability: classical, statistical, and axiomatic. The classical approach defines probability as the ratio of favorable cases to total possible cases. The statistical approach determines probabilities based on empirical observations over many trials. The axiomatic approach uses set theory and axioms to define probability without restrictions of previous approaches.

Probability

Probability not Higher Level....This PPT is for beginners or for those who learnt or to study PROBABILITY........... :):):):):)

Probability Concepts

classical, empirical, and subjective
approaches to probability.conditional probability and joint
probability.Bayes’ theorem.

Probability

The document discusses probability and set theory. It defines probability as a quantitative measure of uncertainty or a measure of degree of belief in a statement. It states that probability is measured on a scale from 0 to 1, where 0 is impossibility and 1 is certainty. It then discusses key concepts in set theory such as sets, subsets, Venn diagrams, and operations on sets like union, intersection, difference, and complement. Finally, it discusses definitions of probability including the classical, relative frequency, and axiomatic definitions.

Basic Elements of Probability Theory

This document provides an overview of basic probability theory concepts including probability, mutually exclusive events, and independence. It discusses probability as a measure of likelihood between 0 and 1. Key concepts covered include interpretations of probability, the mathematical treatment including independent, conditional, and summary probabilities, and applications in areas like reliability and natural language processing. Mutually exclusive events are defined as events that cannot occur simultaneously, while independent events have probabilities that are unaffected by each other.

vinayjoshi-131204045346-phpapp02.pdf

This document provides an introduction to probability. It defines probability as a measure of how likely an event is to occur. Probability is expressed as a ratio of favorable outcomes to total possible outcomes. The key terms used in probability are defined, including event, outcome, sample space, and elementary events. The theoretical approach to probability is discussed, where probability is predicted without performing the experiment. Random experiments are described as those that may not produce the same outcome each time. Laws of probability are presented, such as a probability being between 0 and 1. Applications of probability in everyday life are mentioned, such as reliability testing of products. Two example probability problems are worked out.

Probability

This document provides an overview of key concepts in probability theory, including:
1. It defines probability as a measure between 0 and 1 of the likelihood of an event occurring or a statement being true.
2. It discusses applications of probability theory in areas like risk assessment and financial markets.
3. It outlines some common probability experiments like coin tosses, dice rolls, and cricket games and identifies their possible experimental outcomes.

Triola t11 chapter4

This document summarizes key concepts from Chapter 4 on probability, including the addition rule, multiplication rule, conditional probability, dependent and independent events, and applying these concepts to calculate probabilities. The chapter covers basic probability concepts like sample spaces, events, and computing probabilities using relative frequency, classical, and subjective approaches. It also discusses odds, complementary events, and using simulations and counting to calculate probabilities.

Probability

The document provides an overview of key probability concepts including:
1. Random experiments, sample spaces, events, and the classification of events as simple, mutually exclusive, independent, and exhaustive.
2. The three main approaches to defining probability: classical, relative frequency, and subjective.
3. Important probability theorems like the addition rule, multiplication rule, and Bayes' theorem.
4. How to calculate probabilities of events using these theorems, including examples of finding probabilities of independent, dependent, mutually exclusive, and conditional events.

Basic Concept Of Probability

1. The document discusses basic concepts in probability and statistics, including sample spaces, events, probability distributions, and random variables.
2. Key concepts are explained such as independent and conditional probability, Bayes' theorem, and common probability distributions like the uniform and normal distributions.
3. Statistical analysis methods are introduced including how to estimate the mean and variance from samples from a distribution.

Basic concepts of probability

This document discusses basic concepts of probability, including:
- The addition rule and multiplication rule for calculating probabilities of compound events.
- Events can be disjoint (mutually exclusive) or not disjoint.
- The probability of an event occurring or its complement must equal 1.
- How to calculate the probability of at least one occurrence of an event using the complement.
- When applying the multiplication rule, you must consider whether events are independent or dependent.

Sample Space and Event,Probability,The Axioms of Probability,Bayes Theorem

The document discusses key concepts in statistics including:
- A sample space contains all possible outcomes of an experiment and events are subsets of the sample space.
- Probability is a branch of mathematics that quantifies the likelihood of events based on the sample space.
- The axioms of probability establish rules like probabilities being between 0 and 1 and the probability of the entire sample space being 1.
- Bayes' theorem calculates conditional probabilities and allows updating probabilities as new evidence becomes available.

Probability

This document defines key concepts in probability and provides examples. It discusses probability vocabulary like sample space, outcome, trial, and event. It defines probability as the number of times a desired outcome occurs over total trials. Events are independent if the outcome of one does not impact others, and mutually exclusive if they cannot occur together. The addition and multiplication rules for probability are explained. Conditional probability describes the probability of a second event depending on the first occurring. Counting techniques are discussed for finding total possible outcomes of combined experiments. Review questions are provided to test understanding of the material.

Probability theory good

This document discusses probability and its key concepts. It begins by defining probability as a quantitative measure of uncertainty ranging from 0 to 1. Probability can be understood objectively based on problems or subjectively based on beliefs. Key probability concepts discussed include:
- Sample space, simple events, and compound events
- Classical, relative frequency, and subjective approaches to assigning probabilities
- Complement, intersection, and union of events
- Conditional probability and independence of events
- Rules for calculating probabilities of combined events like the multiplication rule
Examples are provided to illustrate concepts like defining sample spaces, calculating probabilities of individual and combined events, determining conditional probabilities, and assessing independence. Overall, the document provides a comprehensive overview of fundamental probability

PROBABILITY AND IT'S TYPES WITH RULES

This document discusses types of probability and provides definitions and examples of key probability concepts. It begins with an introduction to probability theory and its applications. The document then defines terms like random experiments, sample spaces, events, favorable events, mutually exclusive events, and independent events. It describes three approaches to measuring probability: classical, frequency, and axiomatic. It concludes with theorems of probability and references.

Probablity distribution

This document discusses probability distributions and provides examples of calculating probabilities using binomial distributions. It begins by defining a probability distribution as a table, graph or formula used to specify the possible values and probabilities of a discrete random variable. It then gives examples of probability distributions for number of assistance programs used by families and calculates related probabilities. The document introduces binomial distribution and provides two examples of calculating probabilities of outcomes for binomial processes, such as number of full term births out of total births. It describes key concepts like Bernoulli trials, processes and use of combinations and factorials to calculate probabilities for larger sample sizes.

Probability

This document discusses key concepts in probability. It defines basic terms like experiment, sample space, event, and probability. It provides examples of calculating probability for coin tosses and dice rolls using the classical method of dividing the number of ways an event can occur by the total number of possible outcomes. The document also discusses limitations of the classical method and introduces the empirical and subjective methods of determining probability based on observed frequencies and personal judgment respectively.

Different types of distributions

This document provides an introduction to probability theory and different probability distributions. It begins with defining probability as a quantitative measure of the likelihood of events occurring. It then covers fundamental probability concepts like mutually exclusive events, additive and multiplicative laws of probability, and independent events. The document also introduces random variables and common probability distributions like the binomial, Poisson, and normal distributions. It provides examples of how each distribution is used and concludes with characteristics of the normal distribution.

Chapter 6 Probability

Chapter 6 ProbabilitySchool of Design Engineering Fashion & Technology (DEFT), University of Wales, Newport

The following presentation is an introduction to the Algebraic Methods – part one for level 4 Mathematics. This resources is a part of the 2009/2010 Engineering (foundation degree, BEng and HN) courses from University of Wales Newport (course codes H101, H691, H620, HH37 and 001H). This resource is a part of the core modules for the full time 1st year undergraduate programme.
The BEng & Foundation Degrees and HNC/D in Engineering are designed to meet the needs of employers by placing the emphasis on the theoretical, practical and vocational aspects of engineering within the workplace and beyond. Engineering is becoming more high profile, and therefore more in demand as a skill set, in today’s high-tech world. This course has been designed to provide you with knowledge, skills and practical experience encountered in everyday engineering environments. Probability theory

This document provides an overview of key concepts in probability theory:
- An experiment yields possible outcomes called a sample space. Events are subsets of outcomes. Random variables assign values to outcomes.
- Probability is a measure of certainty that an event will occur, ranging from 0 (impossible) to 1 (certain). It can be defined in different ways.
- The frequentist definition is the limit of relative frequencies of an event over many trials. The Bayesian definition is a degree of belief in an event. The Laplacian definition assumes all outcomes are equally likely initially.
- Examples demonstrate random variables, events, and calculating probabilities based on the sample space and outcomes of an experiment. Key terms like sample space, event,

Probability Theory

The document discusses probability theory and provides definitions and examples of key concepts like conditional probability and Bayes' theorem. It defines probability as the ratio of favorable events to total possible events. Conditional probability is the probability of an event given that another event has occurred. Bayes' theorem provides a way to update or revise beliefs based on new evidence and relates conditional probabilities. Examples are provided to illustrate concepts like conditional probability calculations.

Basic Probability Distribution

The document provides an overview of probability distribution basics, including definitions of key probability concepts like experiments, outcomes, sample space, events, unions, and intersections. It also covers types of probability distributions like discrete and continuous, binomial distribution, Poisson distribution, and normal distribution. Specific examples are given to illustrate probability calculation and the different laws and features of probability distributions.

Basic concepts of probability

1) The document introduces basic concepts of probability such as sample spaces, events, outcomes, and how to calculate classical and empirical probabilities.
2) It discusses approaches to determining probability including classical, empirical, and subjective probabilities. Simulations can also be used to estimate probabilities.
3) Examples are provided to illustrate calculating probabilities using classical and empirical approaches for single and compound events with different sample spaces.

Lecture: Joint, Conditional and Marginal Probabilities

The document discusses joint, conditional, and marginal probabilities. It begins with an introduction to joint and conditional probabilities, defining conditional probability as the probability of event A given event B. It then presents the multiplication rule for calculating joint probabilities from conditional probabilities and marginal probabilities. The document provides examples and calculations to illustrate these probability concepts. It concludes with short quizzes to test understanding of applying the multiplication rule.

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Concept of Measurements in Business Research

Measurement is a fundamental concept in business research used to quantify variables and enable comparison. It requires defining what is to be measured and how through operational definitions. There are four levels of measurement - nominal, ordinal, interval, and ratio - determined by the characteristics of order, distance, and origin represented. Validity and reliability are important criteria for any measurement and various techniques like rating, ranking, and sorting are used depending on whether the concept is simple or complex.

Basic Elements of Probability Theory

This document provides an overview of basic probability theory concepts including probability, mutually exclusive events, and independence. It discusses probability as a measure of likelihood between 0 and 1. Key concepts covered include interpretations of probability, the mathematical treatment including independent, conditional, and summary probabilities, and applications in areas like reliability and natural language processing. Mutually exclusive events are defined as events that cannot occur simultaneously, while independent events have probabilities that are unaffected by each other.

vinayjoshi-131204045346-phpapp02.pdf

This document provides an introduction to probability. It defines probability as a measure of how likely an event is to occur. Probability is expressed as a ratio of favorable outcomes to total possible outcomes. The key terms used in probability are defined, including event, outcome, sample space, and elementary events. The theoretical approach to probability is discussed, where probability is predicted without performing the experiment. Random experiments are described as those that may not produce the same outcome each time. Laws of probability are presented, such as a probability being between 0 and 1. Applications of probability in everyday life are mentioned, such as reliability testing of products. Two example probability problems are worked out.

Probability

This document provides an overview of key concepts in probability theory, including:
1. It defines probability as a measure between 0 and 1 of the likelihood of an event occurring or a statement being true.
2. It discusses applications of probability theory in areas like risk assessment and financial markets.
3. It outlines some common probability experiments like coin tosses, dice rolls, and cricket games and identifies their possible experimental outcomes.

Triola t11 chapter4

This document summarizes key concepts from Chapter 4 on probability, including the addition rule, multiplication rule, conditional probability, dependent and independent events, and applying these concepts to calculate probabilities. The chapter covers basic probability concepts like sample spaces, events, and computing probabilities using relative frequency, classical, and subjective approaches. It also discusses odds, complementary events, and using simulations and counting to calculate probabilities.

Probability

The document provides an overview of key probability concepts including:
1. Random experiments, sample spaces, events, and the classification of events as simple, mutually exclusive, independent, and exhaustive.
2. The three main approaches to defining probability: classical, relative frequency, and subjective.
3. Important probability theorems like the addition rule, multiplication rule, and Bayes' theorem.
4. How to calculate probabilities of events using these theorems, including examples of finding probabilities of independent, dependent, mutually exclusive, and conditional events.

Basic Concept Of Probability

1. The document discusses basic concepts in probability and statistics, including sample spaces, events, probability distributions, and random variables.
2. Key concepts are explained such as independent and conditional probability, Bayes' theorem, and common probability distributions like the uniform and normal distributions.
3. Statistical analysis methods are introduced including how to estimate the mean and variance from samples from a distribution.

Basic concepts of probability

This document discusses basic concepts of probability, including:
- The addition rule and multiplication rule for calculating probabilities of compound events.
- Events can be disjoint (mutually exclusive) or not disjoint.
- The probability of an event occurring or its complement must equal 1.
- How to calculate the probability of at least one occurrence of an event using the complement.
- When applying the multiplication rule, you must consider whether events are independent or dependent.

Sample Space and Event,Probability,The Axioms of Probability,Bayes Theorem

The document discusses key concepts in statistics including:
- A sample space contains all possible outcomes of an experiment and events are subsets of the sample space.
- Probability is a branch of mathematics that quantifies the likelihood of events based on the sample space.
- The axioms of probability establish rules like probabilities being between 0 and 1 and the probability of the entire sample space being 1.
- Bayes' theorem calculates conditional probabilities and allows updating probabilities as new evidence becomes available.

Probability

This document defines key concepts in probability and provides examples. It discusses probability vocabulary like sample space, outcome, trial, and event. It defines probability as the number of times a desired outcome occurs over total trials. Events are independent if the outcome of one does not impact others, and mutually exclusive if they cannot occur together. The addition and multiplication rules for probability are explained. Conditional probability describes the probability of a second event depending on the first occurring. Counting techniques are discussed for finding total possible outcomes of combined experiments. Review questions are provided to test understanding of the material.

Probability theory good

This document discusses probability and its key concepts. It begins by defining probability as a quantitative measure of uncertainty ranging from 0 to 1. Probability can be understood objectively based on problems or subjectively based on beliefs. Key probability concepts discussed include:
- Sample space, simple events, and compound events
- Classical, relative frequency, and subjective approaches to assigning probabilities
- Complement, intersection, and union of events
- Conditional probability and independence of events
- Rules for calculating probabilities of combined events like the multiplication rule
Examples are provided to illustrate concepts like defining sample spaces, calculating probabilities of individual and combined events, determining conditional probabilities, and assessing independence. Overall, the document provides a comprehensive overview of fundamental probability

PROBABILITY AND IT'S TYPES WITH RULES

This document discusses types of probability and provides definitions and examples of key probability concepts. It begins with an introduction to probability theory and its applications. The document then defines terms like random experiments, sample spaces, events, favorable events, mutually exclusive events, and independent events. It describes three approaches to measuring probability: classical, frequency, and axiomatic. It concludes with theorems of probability and references.

Probablity distribution

This document discusses probability distributions and provides examples of calculating probabilities using binomial distributions. It begins by defining a probability distribution as a table, graph or formula used to specify the possible values and probabilities of a discrete random variable. It then gives examples of probability distributions for number of assistance programs used by families and calculates related probabilities. The document introduces binomial distribution and provides two examples of calculating probabilities of outcomes for binomial processes, such as number of full term births out of total births. It describes key concepts like Bernoulli trials, processes and use of combinations and factorials to calculate probabilities for larger sample sizes.

Probability

This document discusses key concepts in probability. It defines basic terms like experiment, sample space, event, and probability. It provides examples of calculating probability for coin tosses and dice rolls using the classical method of dividing the number of ways an event can occur by the total number of possible outcomes. The document also discusses limitations of the classical method and introduces the empirical and subjective methods of determining probability based on observed frequencies and personal judgment respectively.

Different types of distributions

This document provides an introduction to probability theory and different probability distributions. It begins with defining probability as a quantitative measure of the likelihood of events occurring. It then covers fundamental probability concepts like mutually exclusive events, additive and multiplicative laws of probability, and independent events. The document also introduces random variables and common probability distributions like the binomial, Poisson, and normal distributions. It provides examples of how each distribution is used and concludes with characteristics of the normal distribution.

Chapter 6 Probability

Chapter 6 ProbabilitySchool of Design Engineering Fashion & Technology (DEFT), University of Wales, Newport

The following presentation is an introduction to the Algebraic Methods – part one for level 4 Mathematics. This resources is a part of the 2009/2010 Engineering (foundation degree, BEng and HN) courses from University of Wales Newport (course codes H101, H691, H620, HH37 and 001H). This resource is a part of the core modules for the full time 1st year undergraduate programme.
The BEng & Foundation Degrees and HNC/D in Engineering are designed to meet the needs of employers by placing the emphasis on the theoretical, practical and vocational aspects of engineering within the workplace and beyond. Engineering is becoming more high profile, and therefore more in demand as a skill set, in today’s high-tech world. This course has been designed to provide you with knowledge, skills and practical experience encountered in everyday engineering environments. Probability theory

This document provides an overview of key concepts in probability theory:
- An experiment yields possible outcomes called a sample space. Events are subsets of outcomes. Random variables assign values to outcomes.
- Probability is a measure of certainty that an event will occur, ranging from 0 (impossible) to 1 (certain). It can be defined in different ways.
- The frequentist definition is the limit of relative frequencies of an event over many trials. The Bayesian definition is a degree of belief in an event. The Laplacian definition assumes all outcomes are equally likely initially.
- Examples demonstrate random variables, events, and calculating probabilities based on the sample space and outcomes of an experiment. Key terms like sample space, event,

Probability Theory

The document discusses probability theory and provides definitions and examples of key concepts like conditional probability and Bayes' theorem. It defines probability as the ratio of favorable events to total possible events. Conditional probability is the probability of an event given that another event has occurred. Bayes' theorem provides a way to update or revise beliefs based on new evidence and relates conditional probabilities. Examples are provided to illustrate concepts like conditional probability calculations.

Basic Probability Distribution

The document provides an overview of probability distribution basics, including definitions of key probability concepts like experiments, outcomes, sample space, events, unions, and intersections. It also covers types of probability distributions like discrete and continuous, binomial distribution, Poisson distribution, and normal distribution. Specific examples are given to illustrate probability calculation and the different laws and features of probability distributions.

Basic concepts of probability

1) The document introduces basic concepts of probability such as sample spaces, events, outcomes, and how to calculate classical and empirical probabilities.
2) It discusses approaches to determining probability including classical, empirical, and subjective probabilities. Simulations can also be used to estimate probabilities.
3) Examples are provided to illustrate calculating probabilities using classical and empirical approaches for single and compound events with different sample spaces.

Lecture: Joint, Conditional and Marginal Probabilities

The document discusses joint, conditional, and marginal probabilities. It begins with an introduction to joint and conditional probabilities, defining conditional probability as the probability of event A given event B. It then presents the multiplication rule for calculating joint probabilities from conditional probabilities and marginal probabilities. The document provides examples and calculations to illustrate these probability concepts. It concludes with short quizzes to test understanding of applying the multiplication rule.

Basic Elements of Probability Theory

Basic Elements of Probability Theory

vinayjoshi-131204045346-phpapp02.pdf

vinayjoshi-131204045346-phpapp02.pdf

Probability

Probability

Triola t11 chapter4

Triola t11 chapter4

Probability

Probability

Basic Concept Of Probability

Basic Concept Of Probability

Basic concepts of probability

Basic concepts of probability

Sample Space and Event,Probability,The Axioms of Probability,Bayes Theorem

Sample Space and Event,Probability,The Axioms of Probability,Bayes Theorem

Probability

Probability

Probability theory good

Probability theory good

PROBABILITY AND IT'S TYPES WITH RULES

PROBABILITY AND IT'S TYPES WITH RULES

Probablity distribution

Probablity distribution

Probability

Probability

Different types of distributions

Different types of distributions

Chapter 6 Probability

Chapter 6 Probability

Probability theory

Probability theory

Probability Theory

Probability Theory

Basic Probability Distribution

Basic Probability Distribution

Basic concepts of probability

Basic concepts of probability

Lecture: Joint, Conditional and Marginal Probabilities

Lecture: Joint, Conditional and Marginal Probabilities

Scientific Writing

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Concept of Measurements in Business Research

Measurement is a fundamental concept in business research used to quantify variables and enable comparison. It requires defining what is to be measured and how through operational definitions. There are four levels of measurement - nominal, ordinal, interval, and ratio - determined by the characteristics of order, distance, and origin represented. Validity and reliability are important criteria for any measurement and various techniques like rating, ranking, and sorting are used depending on whether the concept is simple or complex.

Business Research and Report Presentation Part 5

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Lec 02 2015 electromagnetic

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2) Research design determines the appropriate research method such as surveys, experiments, or secondary data analysis.
3) Data gathering involves sampling, collection of primary or secondary data.
4) Data analysis and processing interprets the findings.
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Electromagnetic Theory

Electromagnetic Theory Full On Electrical & Electronics Engineering Core Subject Basics As Well As In Depth.
-Prabhaharan429

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2) Maxwell's equations relate electric and magnetic fields to electric charges and currents.
3) The document goes on to describe various electromagnetic concepts like current density, conduction and convection currents, and introduces Maxwell's equations in both differential and integral form.

Quantitative Data Analysis: Hypothesis Testing

This document provides an overview of quantitative data analysis techniques for hypothesis testing, including types of errors, statistical power, and tests for single and multiple sample means. It also discusses regression analysis, issues of multicollinearity, and other multivariate tests such as discriminant analysis, logistic regression, and canonical correlation.

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By
Dr. Muhammad Ramzan
mramzaninfo@gmail.com,
03004487844
Edited by Ahsan Khan Eco
ahsankhaneco@yahoo.com
03008046243

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This document discusses research ethics and plagiarism. It presents four cases involving ethical issues in research: 1) Authorship disputes between a professor and PhD student on a grant-funded study. 2) A doctor considering manipulating data from an interim analysis of a clinical trial. 3) A doctor unsure about participating in an international drug trial. 4) Issues with the informed consent process for a drug safety study. It also provides background on regulations put in place after tragic human experiments and discusses principles of ethical research from the Nuremberg Code.

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- Statistical hypothesis testing involves a null hypothesis (H0) and alternative hypothesis (Ha). H0 is the initial assumption being tested, while Ha is what would be accepted if H0 is rejected.
- Type I errors incorrectly reject a true null hypothesis. Type II errors fail to reject a false null hypothesis. Hypothesis tests aim to control the probability of type I errors.
- The significance level is the probability of a type I error,

Hypothesis testing ppt final

This document provides an overview of hypothesis testing in inferential statistics. It defines a hypothesis as a statement or assumption about relationships between variables or tentative explanations for events. There are two main types of hypotheses: the null hypothesis (H0), which is the default position that is tested, and the alternative hypothesis (Ha or H1). Steps in hypothesis testing include establishing the null and alternative hypotheses, selecting a suitable test of significance or test statistic based on sample characteristics, formulating a decision rule to either accept or reject the null hypothesis based on where the test statistic value falls, and understanding the potential for errors. Key criteria for constructing hypotheses and selecting appropriate statistical tests are also outlined.

Types of hypotheses

The document discusses different types of hypotheses:
- Directional hypotheses specify the expected direction of relationships between variables, while non-directional hypotheses do not.
- Hypotheses can take declarative, null, question, or predictive forms. Declarative hypotheses state expected relationships, while null hypotheses state no relationship exists. Question hypotheses are research questions. Predictive hypotheses allow researchers to state expected principles.
- Examples are provided for each type to illustrate their meanings.

RESEARCH METHOD - SAMPLING

This was a presentation that was carried out in our research method class by our group. It will be useful for PHD and master students quantitative and qualitative method. It consist sample definition, purpose of sampling, stages in the selection of a sample, types of sampling in quantitative researches, types of sampling in qualitative researches, and ethical Considerations in Data Collection.

Scientific Writing

Scientific Writing

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Concept of Measurements in Business Research

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Business Research and Report Presentation Part 5

Lec 02 2015 electromagnetic

Lec 02 2015 electromagnetic

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Business research-process

Electromagnetic Theory

Electromagnetic Theory

Electromagnetic Theory notes

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Electromagnetic Theory

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Quantitative Data Analysis: Hypothesis Testing

Quantitative Data Analysis: Hypothesis Testing

Electromagnetic theory

Electromagnetic theory

Business Research Methods. data collection preparation and analysis

Business Research Methods. data collection preparation and analysis

business research process, design and proposal

business research process, design and proposal

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Primary and Secondary Data collection - Ajay Anoj & Gokul

Research ethics

Research ethics

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Probability concept and Probability distribution

Hypothesis

Hypothesis

Test of hypothesis

Test of hypothesis

Hypothesis testing ppt final

Hypothesis testing ppt final

Types of hypotheses

Types of hypotheses

RESEARCH METHOD - SAMPLING

RESEARCH METHOD - SAMPLING

4 1 probability and discrete probability distributions

This document discusses probabilities and probability distributions. It begins by defining an experiment and sample space. A random variable is defined as a numerical value determined by the outcome of an experiment. Random variables can be discrete or continuous. Probability distributions show all possible outcomes of an experiment and their probabilities. The binomial distribution is discussed as modeling discrete experiments with binary outcomes and fixed probabilities. Key properties of the binomial include the mean, variance, and use of the binomial probability formula and tables to calculate probabilities of various outcomes.

Machine learning session2

In this slide, variables types, probability theory behind the algorithms and its uses including distribution is explained. Also theorems like bayes theorem is also explained.

Testing hypothesis

This document provides an overview of key concepts in hypothesis testing including:
- The null and alternative hypotheses, where the null hypothesis is what we aim to reject or fail to reject.
- The level of significance and critical region, which define the threshold for rejecting the null hypothesis.
- Type I and type II errors, where we aim to minimize both by choosing an appropriate significance level and critical region.
- Common test statistics like z, t, and chi-squared that are used to evaluate hypotheses based on samples.
- The process of hypothesis testing, which involves defining hypotheses, choosing a test statistic and significance level, and making a decision to reject or fail to reject the null based on the critical region.

4Probability and probability distributions.pdf

Here are the key steps to solve this problem:
1) Draw the standard normal curve
2) The probability is the area between -2.55 and 2.55
3) From the standard normal table:
P(Z ≤ 2.55) = 0.9938
P(Z ≤ -2.55) = 0.0049
4) Use the area property:
P(-2.55 ≤ Z ≤ 2.55) = P(Z ≤ 2.55) - P(Z ≤ -2.55)
= 0.9938 - 0.0049
= 0.9889
Therefore, the probability that a z value will be between -2.55 and 2

Statistical analysis by iswar

This ppt is prepared according to RGUHS syllabus, Modern Pharmaceutical analysis for 1st year M.pharm students

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This document discusses inferential statistics and epidemiological research. It introduces concepts like the central limit theorem, standard error, confidence intervals, hypothesis testing, and different statistical tests. Specifically, it covers:
- The central limit theorem states that sample means will follow a normal distribution, even if the population is not normally distributed.
- Standard error is used to measure sampling variation and determine confidence intervals around sample statistics to estimate population parameters.
- Hypothesis testing involves a null hypothesis of no difference and an alternative hypothesis of a significant difference.
- Common tests discussed include chi-square tests to compare proportions between groups and determine if differences are significant.

Module-2_Notes-with-Example for data science

The document discusses several key concepts in probability and statistics:
- Conditional probability is the probability of one event occurring given that another event has already occurred.
- The binomial distribution models the probability of success in a fixed number of binary experiments. It applies when there are a fixed number of trials, two possible outcomes, and the same probability of success on each trial.
- The normal distribution is a continuous probability distribution that is symmetric and bell-shaped. It is characterized by its mean and standard deviation. Many real-world variables approximate a normal distribution.
- Other concepts discussed include range, interquartile range, variance, and standard deviation. The interquartile range describes the spread of a dataset's middle 50%

Statistics78 (2)

1. The document summarizes key concepts from a lecture on statistics for engineers, including the normal distribution, the central limit theorem, and normal approximations to the binomial and Poisson distributions.
2. It provides an example of using the normal approximation to the Poisson distribution to calculate how many pills should be ordered to ensure the probability of running out is less than 0.005.
3. The document cautions that normal approximations may provide inaccurate results if assumptions like independence are violated, as with infectious diseases. Simple approximations are not advisable if failure could have important consequences, as with estimating rare event probabilities.

Normal Distribution

A general overview of Normal distribution, Standard Normal Distribution, and relevant Examples to calculate.

Test of-significance : Z test , Chi square test

1) Tests of significance help determine if observed differences between samples are real or due to chance. The null hypothesis assumes no real difference, and significance tests either reject or fail to reject the null hypothesis.
2) Common tests include the Z-test for comparing two proportions, and the chi-square test which can be used for both large and small samples to compare observed and expected frequencies across groups.
3) To perform a significance test, the null hypothesis is stated, a test statistic is calculated (like Z or chi-square), and the p-value determines whether to reject or fail to reject the null hypothesis at a given significance level like 5%.

Biostatistics

This document provides an overview of biostatistics and various statistical concepts used in dental sciences. It discusses measures of central tendency including mean, median, and mode. It also covers measures of dispersion such as range, mean deviation, and standard deviation. The normal distribution curve and properties are explained. Various statistical tests are mentioned including t-test, ANOVA, chi-square test, and their applications in dental research. Steps for testing hypotheses and types of errors are summarized.

Decision Sciences_SBS_10.pdf

This document provides an introduction to probability theory and probability distributions. It defines key probability concepts like random experiments, outcomes, sample space, mutually exclusive and collectively exhaustive events. It then covers probability calculations, addition of probabilities, conditional probability, Bayes' theorem, and the binomial, Poisson and normal probability distributions. Several examples are provided to demonstrate applying these probability concepts.

PG STAT 531 Lecture 5 Probability Distribution

This document provides an overview of probability distributions including binomial, Poisson, and normal distributions. It discusses key concepts such as:
- Binomial distributions describe experiments with two possible outcomes and fixed number of trials.
- Poisson distributions model rare events with sample sizes so large one outcome is much more common.
- Normal distributions produce bell-shaped curves defined by the mean and standard deviation. They are widely used in statistics.

MD Paediatricts (Part 2) - Epidemiology and Statistics

The document discusses various study designs used in epidemiology and statistics, including observational and experimental designs. It provides details on descriptive and analytical observational studies. Descriptive studies generate hypotheses, while analytical studies allow determination of causal associations by including a comparison or control group. Experimental designs are randomized studies that can establish causal relationships. The document also covers topics like odds ratios, relative risks, attributable risks, chi-square tests, sensitivity and specificity in diagnostic testing.

2.statistical DEcision makig.pptx

This document discusses statistical decision making and various statistical classification techniques. It introduces Bayes' theorem and how it can be used for classification when the joint probability is difficult to calculate. It discusses parametric and non-parametric decision making methods. It also covers topics like decision trees, entropy, histograms, k-nearest neighbor classification, and decision boundaries. Examples of applying Bayes' theorem to medical diagnosis problems are provided.

Sriram seminar on introduction to statistics

The document provides an introduction to statistics concepts including central tendency, dispersion, probability, and random variables. It discusses different measures of central tendency like mean, median and mode. It also covers dispersion concepts like variance and standard deviation. The document introduces key probability concepts such as experiments, sample spaces, events, and conditional probability. It defines random variables and discusses discrete and continuous random variables.

Tbs910 sampling hypothesis regression

This document discusses sampling, hypothesis testing, and regression. It covers topics such as using samples to estimate population parameters, sampling distributions, calculating confidence intervals for means and proportions, hypothesis testing using sampling distributions, and simple linear regression. The key points are that sampling is used for statistical inference about populations, sampling distributions describe the variation in sample statistics, and confidence intervals and hypothesis tests allow making inferences with a known degree of confidence or significance.

statistics

This document provides an introduction to inferential statistics and statistical significance. It discusses key concepts like standard error of the mean, confidence intervals, and comparing means from two samples using a t-test. The document explains how inferential statistics allow researchers to make inferences about populations based on samples and determine if observed differences are likely due to chance or a real effect.

Test of significance

The document provides an overview of statistical hypothesis testing and various statistical tests used to analyze quantitative and qualitative data. It discusses types of data, key terms like null hypothesis and p-value. It then outlines the steps in hypothesis testing and describes different tests of significance including standard error of difference between proportions, chi-square test, student's t-test, paired t-test, and ANOVA. Examples are provided to demonstrate how to apply these statistical tests to determine if differences observed in sample data are statistically significant.

Inorganic CHEMISTRY

This document provides an outline and summaries of topics related to error analysis:
- It outlines topics including binomial distribution, Poisson distribution, normal distribution, confidence interval, and least squares analysis.
- The binomial distribution section provides an example of calculating the probability of getting 2 and 3 heads out of 6 coin tosses.
- The normal distribution section explains how to calculate the probability of scoring between 90-110 on an IQ test with a mean of 100 and standard deviation of 10.
- The confidence interval section provides an example of calculating the 95% confidence interval for the population mean boiling temperature based on 6 sample measurements.

4 1 probability and discrete probability distributions

4 1 probability and discrete probability distributions

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Machine learning session2

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Testing hypothesis

4Probability and probability distributions.pdf

4Probability and probability distributions.pdf

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Biostatistics ii4june

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PG STAT 531 Lecture 5 Probability Distribution

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MD Paediatricts (Part 2) - Epidemiology and Statistics

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2.statistical DEcision makig.pptx

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Sriram seminar on introduction to statistics

Sriram seminar on introduction to statistics

Tbs910 sampling hypothesis regression

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statistics

statistics

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Biases

This document discusses various types of bias that can occur in research studies. It defines bias as an unknown or unacknowledged error created during the research process. Some key biases discussed include selection bias, measurement bias, confounding, and publication bias. The document emphasizes the importance of research design features like randomization and blinding to help reduce bias.

Biostatistics II

This document provides an overview of key concepts in biostatistics including:
- Random and systematic error and how they can lead to incorrect results
- Different types of validity in measurements including content, face, construct, and criterion-related validity
- The role of confounding variables and how they can influence exposure and disease relationships
- Common hypotheses for statistical tests including the null and alternative hypotheses
- Types of errors like type I (false positive) and type II (false negative) errors
- When to use parametric vs non-parametric tests based on sample size and data distribution
- Assumptions of the t-test and examples of the t-test, Mann-Whitney, and Wilcoxon signed

Introduction to biostatistics

Introduction to biostatistics lecture by Prof. Faisal Farahat, as part of the 5th Research Summer School - Jeddah held by KAIMRC - WR

Reliability and validity

Reliability and validity by Dr. Hatim Al-Jifri as part of the 5th Research Summer School - Jeddah at KAIMRC - WR

Formulation of research questions

The document provides guidance on formulating a research question. It discusses identifying a research problem or opportunity and determining the unit of analysis. It also covers translating the research problem into a research question and formulating a hypothesis to be tested. Well-formulated research questions are answerable, specific, measurable, and linked to a theoretical framework. The goal is to develop a question that will focus the research and facilitate subsequent steps in the research process.

Hypothesis testing

This document discusses hypothesis testing, which involves drawing inferences about a population based on a sample from that population. It outlines the key elements of a hypothesis test, including the null and alternative hypotheses, test statistics, critical regions, significance levels, critical values, and p-values. Type I and Type II errors are explained, where a Type I error involves rejecting the null hypothesis when it is true, and a Type II error involves failing to reject the null when it is false. The power of a hypothesis test is defined as the probability of correctly rejecting the null hypothesis when it is false. Controlling type I and II errors involves considering the significance level, sample size, and population parameters in the null and alternative hypotheses.

Questionnaire design & basic of survey

Questionnaire design & basic of survey by Dr. Badr Aljaser as part of the 5th Research Summer School at KAIMRC

RSS study design

This document discusses different types of epidemiological study designs, including descriptive and experimental designs. Descriptive designs include cross-sectional studies, case reports, case series, and qualitative studies. Cross-sectional studies examine the relationship between diseases and other factors in a population at a single point in time. Case reports and case series describe characteristics of individual patients or small groups. Experimental designs include randomized controlled trials (RCTs) which test the effectiveness of interventions by randomly assigning participants to intervention or control groups. Observational studies like case-control and cohort studies examine the relationship between exposures and outcomes without intervention. The document outlines advantages and disadvantages of each design.

Literature reviews & literature searches

This document discusses conducting literature reviews and searches. It begins by defining a literature review and outlining important steps, including selecting research questions, choosing search terms, applying screening criteria, and critically appraising sources. Several databases and types of sources are identified for literature searches. Key steps in the search process involve breaking questions into concepts, identifying subject headings and synonyms, and combining searches with Boolean operators. Criteria for critically evaluating search results from journals, articles, and websites are also provided.

Social media RSS5

Social media RSS5, by Dr. Moaath Saggaf, explaining the use of social media and collaboration tools in RSS5

Writing research proposal

This document discusses the key elements of writing a successful research proposal. It explains that a proposal should include an introduction stating the research problem, a literature review to establish the context and need for the study, clearly defined objectives, a detailed methodology section, a work plan with timeline, and intended dissemination of results. The document cautions common mistakes like lack of focus, unclear or weak arguments, and improper referencing. Overall, the document provides guidance on how to structure a proposal to obtain approval and funding for a research study.

Introduction to research and developing research idea

The document discusses research planning and methods. It describes identifying a knowledge gap and formulating a research question. Key aspects of a good research question are that it is important, innovative, answerable, and worth answering. The document contrasts background and foreground clinical questions. It emphasizes formulating questions focused on a specific problem, intervention, comparator, and outcome. Different study types - observational (descriptive, analytical) and interventional - are outlined, including their advantages and disadvantages. Cross-sectional, cohort, and case-control observational study designs are described in detail.

Study designs 2013

This document provides an overview of different study designs used in epidemiology and biomedical research. It begins by distinguishing between observational and experimental studies. The main types of observational studies covered are case-control, cohort, cross-sectional, and ecological studies. Experimental studies discussed are randomized controlled trials. Key characteristics, advantages, and disadvantages of each study design are outlined. Examples are provided to illustrate concepts.

RSS5 Student Perspective - Jeddah

The document provides details about the 5th Research Summer School (RSS) including an overview of the course timeline and research project process, profiles of the student coordinators, highlights of projects from the previous year including achievements and awards, advantages and challenges of participating in RSS, expectations for the current year, important dates, and information about the RSS Jeddah app and using social media to engage with the program.

New research proposal form

This document appears to be a research proposal application form for the King Abdullah International Medical Research Center and King Saud Bin Abdulaziz University for Health Sciences. It requests information about the proposed research study including the title, investigators, objectives, methodology, timeline, and budget. The proposal form provides instructions for completing each section and requests details on the background, study design, sampling, data collection/analysis, references, workplan, and appendices. It emphasizes that the proposal should justify the public health importance and provide a literature review to support the study.

Research contract

This document is a research contract between a student and their primary and secondary supervisors for the 5th Research Summer School 2013 hosted by the King Abdullah International Medical Research Center. The contract details the proposed research project including the title, objectives, methodology, significance, rationale, and logistics. It requires signatures from the student and supervisors to approve the proposal and timeline for completion by the end of the summer school.

5th rss 2013 program

This document outlines the schedule and activities for a 6-week research skills summer program hosted by the King Abdullah International Medical Research Center. The program includes lectures on developing research questions, study designs, literature reviews, proposal writing, data collection and management, biostatistics, and presenting research. Participants will work with mentors to formulate a research proposal, collect and analyze data, and present their findings at the end of the program. The goal is to provide trainees with hands-on experience in conducting and communicating medical research.

Biases

Biases

Biostatistics II

Biostatistics II

Introduction to biostatistics

Introduction to biostatistics

Reliability and validity

Reliability and validity

Formulation of research questions

Formulation of research questions

Hypothesis testing

Hypothesis testing

Questionnaire design & basic of survey

Questionnaire design & basic of survey

RSS study design

RSS study design

Literature reviews & literature searches

Literature reviews & literature searches

Social media RSS5

Social media RSS5

Writing research proposal

Writing research proposal

Introduction to research and developing research idea

Introduction to research and developing research idea

Study designs 2013

Study designs 2013

RSS5 Student Perspective - Jeddah

RSS5 Student Perspective - Jeddah

New research proposal form

New research proposal form

Research contract

Research contract

5th rss 2013 program

5th rss 2013 program

Stack Memory Organization of 8086 Microprocessor

The stack memory organization of 8086 microprocessor.

Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"

Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"National Information Standards Organization (NISO)

This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.Standardized tool for Intelligence test.

ASSESSMENT OF INTELLIGENCE USING WITH STANDARDIZED TOOL

HYPERTENSION - SLIDE SHARE PRESENTATION.

IT WILL BE HELPFULL FOR THE NUSING STUDENTS
IT FOCUSED ON MEDICAL MANAGEMENT AND NURSING MANAGEMENT.
HIGHLIGHTS ON HEALTH EDUCATION.

Nutrition Inc FY 2024, 4 - Hour Training

Slides for Lessons: Homes and Centers

Wound healing PPT

This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.

Pharmaceutics Pharmaceuticals best of brub

First year pharmacy
Best for u

How to Setup Warehouse & Location in Odoo 17 Inventory

In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.

Haunted Houses by H W Longfellow for class 10

Haunted Houses by H W Longfellow for class 10 ICSE

Benner "Expanding Pathways to Publishing Careers"

This presentation was provided by Rebecca Benner, Ph.D., of the American Society of Anesthesiologists, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.

BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...

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https://app.box.com/s/qhtvq32h4ybf9t49ku85x0n3xl4jhr15Pengantar Penggunaan Flutter - Dart programming language1.pptx

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MDP on air pollution of class 8 year 2024-2025

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Leveraging Generative AI to Drive Nonprofit Innovation

In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)

math operations ued in python and all used

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ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...

Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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BBR 2024 Summer Sessions Interview Training

Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams

How to Predict Vendor Bill Product in Odoo 17

This slide will guide us through the process of predicting vendor bill products based on previous purchases from the vendor in Odoo 17.

Stack Memory Organization of 8086 Microprocessor

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Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"

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Standardized tool for Intelligence test.

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HYPERTENSION - SLIDE SHARE PRESENTATION.

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Wound healing PPT

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Pengantar Penggunaan Flutter - Dart programming language1.pptx

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MDP on air pollution of class 8 year 2024-2025

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BBR 2024 Summer Sessions Interview Training

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How to Predict Vendor Bill Product in Odoo 17

How to Predict Vendor Bill Product in Odoo 17

- 1. PROBABILITY THEORY Oyindamola Bidemi Yusuf
- 2. What is Probability? Measurement of uncertainty Theory of choice and chance Allows intelligence guess about future Helps to quantify risk Predicts outcomes
- 3. PROBABILITY DEFINITION- OBJECTIVE Frequency Concept Based on empirical observations Number of times an event occurs in a long series of trials
- 4. PROBABILITY DEFINITION - SUBJECTIVE Merely expresses degree of belief Based on personal experience
- 5. Basic Terminologies Experiment(Process of conducting trials) Trial (Act of an experiment.) Outcome ( Result of a Particular trial) Event (Particular outcome or single result of an experiment)
- 7. Classical Probability Count number favorable to event E = a Count number unfavorable to event E = b Total favorable and unfavorable = a+b Assume E can occur in n possible ways Assume occurrence of events equally likely Total number of possible ways =a+b = n
- 8. Probability of an event-E Probability of E = a = Pr(E) a+b Number of times event favorable divided by number of all possible ways.
- 9. Probability Thermometer . 1.0 - sure to occur – - 0.5 0- cannot occur 0>Pr (E) < 1
- 10. Type of Events Simple events Compound events Mutually exclusive events Independent events
- 11. Simple events Events with single outcomes tossing a fair coin
- 12. Compound events Compound events is the combination of two or more than two simple events. Suppose two coins are tossed simultaneously
- 14. Addition rule Single 6-sided die is rolled. What is the probability of rolling a 2 or a 5? P(2) = 1/6 P(5) = 1/6 P(2 or 5) = P(2) + P(5) = 1/6 + 1/6 =2/6
- 15. Mutually Exclusive Events Pr (A or B) = Pr (A) + Pr (B) IF not mutually exclusive Pr (A or B) = Pr (A) + Pr (B) - Pr (A and B)
- 16. QUESTION ON MUTUALLY EXLUSIVE EVENTS From the records at an STC, 4 girls had HIV, 4 other girls had gonorrhea while 2 girls have both gonorrhea and HIV. What is the probability that any girl selected will have i. HIV only ii. HIV or Gonorrhea.
- 17. SOLUTION Prob. Of HIV only =4/10 – Prob. of HIV or Gonorrhea = Pr(HIV) + Prob.(Gonorrhea) - Pr(HIV and Gonorrhea) = 4/10 + 4/10 - 2/ 10
- 18. Independent events Choosing a marble from a jar AND landing on heads after tossing a coin. Choosing a 3 from a deck of cards, replacing it, AND then choosing an ace as the second card. Rolling a 4 on a single 6-sided die, AND then rolling a 1 on a second roll of the die.
- 19. Multiplication Rule When two events, A and B, are independent, the probability of both occurring is: P(A and B) = P(A) · P(B)
- 20. A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die. P(head) = 1/2 P(3) = 1/6 P(head & 3) = P(head) · P(3) =1/2 x 1/6 = 1/12
- 21. Conditional Probability In probability theory, a conditional probability is the probability that an event will occur, when another event is known to occur or to have occurred.
- 22. Conditional Probability Events not independent Pr (A given B) = Pr (A and B) Pr (B)
- 23. On the “Information for the Patient” label of a certain antidepressant, it is claimed that based on some clinical trials, there is a 14% chance of experiencing sleeping problems known as insomnia (denote this event by I), 26% chance of experiencing headache (denote this event by H), and there is a 5% chance of experiencing both side effects (I and H).
- 24. Suppose that the patient experiences insomnia; what is the probability that the patient will also experience headache? Since we know (or it is given) that the patient experienced insomnia, we are looking for P(H | I). According to the definition of conditional probability: P(H | I) = P(H and I) / P(I) = 0.05/0.14 = 0.357.
- 25. Random Variables A real valued function, defined over the sample space of a random experiment is called the random variable, associated to that random experiment. That is the values of the random variable correspond to the outcomes of the random experiment.
- 26. Random Variables Take specified values with specified probabilities Discrete Random variable –E.g. no of children in a family, no of patients in a doctors surgery Continuous Random variable
- 27. The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function
- 28. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile, etc
- 30. BINOMIAL DISTRIBUTION Successive trials are independent Only two outcomes are possible in each trial or observation Chance of success in each trial is known Same chance of success from trial to trial
- 31. BINOMIAL FORMULA Pr (r out of n events) = n ! pr qn-r r! (n-r) ! where n ! =n(n-1)(n-2)(n-3)….2.1 e.g. 3! =3x2x1
- 32. BINOMINAL TERMS N = Number of trials r = Number of successes p = Probability of success in each trial q = 1-p = Probability of failure in each trial ! = Factorial sign
- 33. EXAMPLE BINOMINAL It is known that 10% of patients diagnosed to have a condition survive following surgical treatment. What is the chance of 2 people surviving out of 5 diagnosed with the condition and treated surgically.
- 34. Solution
- 36. The Normal Curve
- 39. The Shape of a Distribution Symmetrical – can be divided at the center so that each half is a mirror image of the other Asymmetrical
- 41. Skewness – If a distribution is asymmetric it is either positively skewed or negatively skewed. – A distribution is said to be positively skewed if the values tend to cluster toward the lower end of the scale (that is, the smaller numbers) with increasingly fewer values at the upper end of the scale (that is, the larger numbers).
- 43. With a negatively skewed distribution, most of the values tend to occur toward the upper end of the scale while increasingly fewer values occur toward the lower end.
- 45. Properties of Normal Curve Bell shaped and symmetric about centre Completely determined by its mean and standard deviation Mean, median and mode have same value Total area under curve is 1 (100%). 68% of all observations lie within one standard deviations of the mean. 95% of observations lie within 1.96 standard deviations of the mean value Gives probability of falling within interval if data has normal distribution.
- 46. Importance of Normal Distribution Fits many practical distributions of variables in medicine If variables are not normally distributed, transformation techniques to make them normal exist. Sampling distributions of means and proportions are known to have normal distributions It is the cornerstone of all parametric tests of statistical significance.
- 47. Presentation of Normal Distribution. As a mathematical equation Graph Table
- 48. - 1. Mathematical Equation - 1/2 (x - )2 y = 1___ e 2II II and e are constants is arithmetic mean is standard deviation
- 51. The Standardized normal distribution All normal distributions have same overall shape Peak and spread may be different However markers of 68th and 95Th percentiles will still be located at 1 and 2 SD This attribute allows for standardization of any normal distribution
- 52. Can define distance along x axis in terms of SD from the mean instead of the true data point Condenses all normal distributions into one through a mathematical equation Z= x- μ σ
- 53. Each data point is converted into a standardized value, and its new value is called a Z score
- 54. Z Score Standardizing data on one scale so that a comparison can be made Standard score or Z score is: – The number of standard deviations from the mean convert a value to a Standard Score: – first subtract the mean, – then divide by the Standard Deviation
- 55. Z Score The z-score is associated with the normal distribution and it is a number that may be used to: – tell you where a score lies compared with the rest of the data, above/below mean. – compare scores from different normal distributions
- 56. Table of Area Areas under a standard normal curve Gives probability of falling within an interval. Standard normal curve has a mean = 0 and standard deviation = 1 Need to transform data to standard normal curve to use this table.
- 57. 1. Transformation to standard Normal Curve. - Use Z = (x - ) Z is standardized normal deviate or normal score. - Read corresponding area from table. - Z is in the Ist column in the table. - Area in the heart of the table.
- 58. The IQs of a group of students are normally distributed with a mean of 100 and a standard deviation of 12. What percentage of students will have an IQ of 110 or more?
- 59. Z= x- μ/ σ Z= (110-100)/12 Z=0.83, this corresponds to 0.2033 from the table 20% of students will have an IQ of 100 or more What % of students will have IQ between 100 and 110?
- 60. If the heights of a population of men are approximately normally distributed with mean of 172m and standard deviation of 6.7cm. What proportion of men would have heights above 180cm.
- 61. solution Z= x- µ σ 180-172 = 1.19 6.7 In the table of normal distribution, the probability of obtaining a standardised normal deviate greater than 1.19 is 0.117(11.7%)
- 62. Therefore around 12% of the population would have heights above 180cm.
- 63. In summary Normal distribution as a predictor of events Direct applications in statistics Testing for significance Backbone of inferential statistics
- 64. THANK YOU