1. The chapter discusses probability distributions of discrete random variables and provides examples.
2. A binomial distribution models experiments with a fixed number of trials, two possible outcomes per trial (success/failure), and a constant probability of success for each trial.
3. For a binomial random variable X with n trials and probability of success π, the mean is nπ and the variance is nπ(1-π).
Determining the Mean, Variance, and Standard Deviation of a Discrete Random Variable
Visit the website for more services: https://cristinamontenegro92.wixsite.com/onevs
This document provides information about binomial and Poisson distributions. It includes examples of calculating probabilities for binomial distributions using the binomial probability formula and binomial tables. It also provides the key characteristics and formula for the Poisson distribution. The mean, variance and standard deviation are defined for binomial distributions. Examples are provided to demonstrate calculating these values.
The document provides information about binomial probability distributions including:
- Binomial experiments have a fixed number (n) of independent trials with two possible outcomes and a constant probability (p) of success.
- The binomial probability distribution gives the probability of getting exactly x successes in n trials. It is calculated using the binomial coefficient and p and q=1-p.
- The mean, variance and standard deviation of a binomial distribution are np, npq, and √npq respectively.
- Examples demonstrate calculating probabilities of outcomes for binomial experiments and determining if results are significantly low or high using the range rule of μ ± 2σ.
This document discusses several discrete probability distributions:
1. Binomial distribution - For experiments with a fixed number of trials, two possible outcomes, and constant probability of success. The probability of x successes is given by the binomial formula.
2. Geometric distribution - For experiments repeated until the first success. The probability of the first success on the xth trial is p(1-p)^(x-1).
3. Poisson distribution - For counting the number of rare, independent events occurring in an interval. The probability of x events is (e^-μ μ^x)/x!, where μ is the mean number of events.
Binomial and Poission Probablity distributionPrateek Singla
The document discusses binomial and Poisson distributions. Binomial distribution describes random events with two possible outcomes, like success/failure. Poisson distribution models rare, independent events occurring randomly over an interval of time/space. An example calculates the probability of defective thermometers using binomial distribution. It also fits a Poisson distribution to automobile accident data from a 50-day period.
2 Review of Statistics. 2 Review of Statistics.WeihanKhor2
This document provides an overview of discrete probability distributions, including the binomial and Poisson distributions.
1) It defines key concepts such as random variables, probability mass functions, and expected value as they relate to discrete random variables. 2) The binomial distribution describes independent Bernoulli trials with a constant probability of success, and is used to calculate probabilities of outcomes from events like coin flips. 3) The Poisson distribution approximates the binomial when the number of trials is large and the probability of success is small. It models rare, independent events with a constant average rate and can be used for problems involving traffic accidents or natural disasters.
If we measure a random variable many times, we can build up a distribution of the values it can take.
Imagine an underlying distribution of values which we would get if it was possible to take more and more measurements under the same conditions.
This gives the probability distribution for the variable.
Make use of the PPT to have a better understanding of Probability Distribution.
Determining the Mean, Variance, and Standard Deviation of a Discrete Random Variable
Visit the website for more services: https://cristinamontenegro92.wixsite.com/onevs
This document provides information about binomial and Poisson distributions. It includes examples of calculating probabilities for binomial distributions using the binomial probability formula and binomial tables. It also provides the key characteristics and formula for the Poisson distribution. The mean, variance and standard deviation are defined for binomial distributions. Examples are provided to demonstrate calculating these values.
The document provides information about binomial probability distributions including:
- Binomial experiments have a fixed number (n) of independent trials with two possible outcomes and a constant probability (p) of success.
- The binomial probability distribution gives the probability of getting exactly x successes in n trials. It is calculated using the binomial coefficient and p and q=1-p.
- The mean, variance and standard deviation of a binomial distribution are np, npq, and √npq respectively.
- Examples demonstrate calculating probabilities of outcomes for binomial experiments and determining if results are significantly low or high using the range rule of μ ± 2σ.
This document discusses several discrete probability distributions:
1. Binomial distribution - For experiments with a fixed number of trials, two possible outcomes, and constant probability of success. The probability of x successes is given by the binomial formula.
2. Geometric distribution - For experiments repeated until the first success. The probability of the first success on the xth trial is p(1-p)^(x-1).
3. Poisson distribution - For counting the number of rare, independent events occurring in an interval. The probability of x events is (e^-μ μ^x)/x!, where μ is the mean number of events.
Binomial and Poission Probablity distributionPrateek Singla
The document discusses binomial and Poisson distributions. Binomial distribution describes random events with two possible outcomes, like success/failure. Poisson distribution models rare, independent events occurring randomly over an interval of time/space. An example calculates the probability of defective thermometers using binomial distribution. It also fits a Poisson distribution to automobile accident data from a 50-day period.
2 Review of Statistics. 2 Review of Statistics.WeihanKhor2
This document provides an overview of discrete probability distributions, including the binomial and Poisson distributions.
1) It defines key concepts such as random variables, probability mass functions, and expected value as they relate to discrete random variables. 2) The binomial distribution describes independent Bernoulli trials with a constant probability of success, and is used to calculate probabilities of outcomes from events like coin flips. 3) The Poisson distribution approximates the binomial when the number of trials is large and the probability of success is small. It models rare, independent events with a constant average rate and can be used for problems involving traffic accidents or natural disasters.
If we measure a random variable many times, we can build up a distribution of the values it can take.
Imagine an underlying distribution of values which we would get if it was possible to take more and more measurements under the same conditions.
This gives the probability distribution for the variable.
Make use of the PPT to have a better understanding of Probability Distribution.
This document discusses discrete probability distributions, specifically the binomial and Poisson distributions. It provides information on calculating probabilities using the binomial and Poisson probability formulas and tables. It defines key characteristics of binomial experiments and conditions for applying the binomial and Poisson distributions. Examples are given to demonstrate calculating probabilities for each distribution, including finding the mean, variance and standard deviation for binomial distributions.
The document discusses discrete and continuous random variables. It defines discrete random variables as variables that can take on countable values, like the number of heads from coin flips. Continuous random variables can take any value within a range, like height. The document explains how to calculate and interpret the mean, standard deviation, and probabilities of events for both types of random variables using examples like Apgar scores for babies and heights of young women.
The central limit theorem states that the sampling distribution of the sample mean x will be approximately normally distributed for sample sizes n greater than 30, regardless of the shape of the population distribution. Specifically, the sampling distribution of x will have a mean equal to the population mean μ and a standard deviation of σ/√n. Similarly, for a sample proportion p, the sampling distribution of p will be approximately normal for n greater than 10 and np and nq both greater than 10, with mean equal to the population proportion p and standard deviation of √(p(1-p)/n).
Probability Distributions for Discrete Variablesgetyourcheaton
This document discusses probability distributions for discrete variables. It begins by defining a probability distribution as a relative frequency distribution of all possible outcomes of an experiment. It provides examples of probability distributions for discrete variables like the binomial distribution. It discusses key aspects of probability distributions like the mean, standard deviation, and different types of distributions like binomial. It provides examples of calculating probabilities, means, and standard deviations for binomial distributions. It discusses the basic characteristics of the binomial distribution and provides an example of constructing a binomial distribution and calculating related probabilities.
This document discusses various probability distributions including the binomial, Poisson, and normal distributions. It provides definitions and formulas for calculating probabilities for each distribution. For the binomial distribution, it covers the binomial probability formula and using the binomial table. For the Poisson distribution, it discusses the Poisson probability formula and Poisson table. It also addresses calculating the mean, variance, and standard deviation for the binomial and Poisson distributions. Finally, it introduces the normal distribution as the most important continuous probability distribution.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 5: Discrete Probability Distribution
5.2 - Binomial Probability Distributions
The document provides information about discrete and continuous random variables:
- It defines discrete and continuous random variables and gives examples of each. A discrete random variable can take countable values while a continuous random variable can take any value in an interval.
- It discusses probability distributions for discrete random variables, including defining the probability distribution and giving examples of how to construct probability distributions from data in tables. It also covers concepts like mean, standard deviation, and cumulative distribution functions.
- Various examples are provided to illustrate how to calculate probabilities, means, standard deviations, and construct probability distributions and cumulative distribution functions from data about discrete random variables. Continuous random variables are also briefly introduced.
GROUP 4 IT-A.pptx ptttt ppt ppt ppt ppt ppt pptZainUlAbedin85
This document discusses discrete random variables and their probability distributions. It defines a discrete random variable as one that has a finite or countable number of possible outcomes that can be listed. It provides examples of discrete and continuous random variables. It then explains how to construct a probability distribution for a discrete random variable by listing the possible outcomes and their probabilities, ensuring the probabilities sum to 1. It also covers how to graph a discrete probability distribution, calculate the mean, variance, and standard deviation of a discrete random variable from its probability distribution.
The document provides information on discrete and continuous random variables as well as discrete probability distributions including the binomial and Poisson distributions. It defines key terms like mean, variance, standard deviation and discusses how to calculate probabilities for these distributions. Examples are provided to demonstrate calculating probabilities for the binomial and Poisson distributions.
1. The Poisson distribution describes the probability of a number of events occurring in a fixed period of time if these events happen with a known average rate and independently of the time since the last event.
2. The Poisson distribution is defined by one parameter, usually denoted by λ, which represents the expected number of events in the given interval of time or space.
3. The probability of observing x events is given by P(X=x) = (e-λ λx)/x!, where e is the base of the natural logarithms.
Probability and Statistics : Binomial Distribution notes ppt.pdfnomovi6416
This document provides an overview of several discrete probability distributions:
- The discrete uniform distribution where each value has an equal probability of 1/k.
- The binomial distribution which models the number of successes in n independent yes/no trials with probability of success p.
- The hypergeometric distribution which models sampling without replacement from a finite population.
- The Poisson distribution which models the number of rare, independent events occurring in a fixed interval of time or space with a constant average rate λ.
Formulas are given for the probability mass functions and key properties like the mean and variance of each distribution. Examples are provided to illustrate calculating probabilities and distribution parameters.
This document defines and provides examples of discrete and continuous random variables. It also introduces key concepts such as:
- Probability mass functions and probability density functions which describe the probabilities associated with different values of discrete and continuous random variables.
- Expected value, which is the average value of a random variable calculated as the sum of each possible value multiplied by its probability.
- Variance, which measures the dispersion of a random variable from its expected value and is calculated using the probability distribution.
- The binomial distribution, which models experiments with a fixed number of trials, two possible outcomes per trial, and fixed probability of success on each trial.
Probability theory discrete probability distributionsamarthpawar9890
This document provides an overview of discrete probability distributions and binomial distributions. It begins by defining random variables and describing discrete and continuous random variables. Examples are given to distinguish between the two. The key aspects of discrete probability distributions are outlined, including how to construct a distribution and calculate measures such as mean, variance, and standard deviation. Binomial experiments are defined as having two possible outcomes, a fixed number of trials, and constant probability of success. The binomial probability formula is presented and used to calculate probabilities in examples.
This document discusses various discrete probability distributions including the binomial and Poisson distributions. It provides examples and formulas for calculating probabilities using these distributions. The key points covered are:
- The binomial distribution describes the probability of successes in a fixed number of yes/no trials where the probability of success is constant. It requires the trials to be independent and have two possible outcomes.
- The Poisson distribution describes the probability of events occurring randomly in time, space or volume. It applies when the number of events is large but the probability of any one event is small.
- Formulas are provided for calculating probabilities using the binomial and Poisson distributions, including the binomial probability formula and Poisson probability formula. Tables can also be used to find binomial and
1) The document discusses concepts from sampling theory including statistical inference, random sampling, sampling distributions, testing hypotheses, errors in hypothesis testing, significance levels, confidence intervals, and the t-distribution.
2) Key points include that statistical inference allows drawing conclusions about a population from a sample, random sampling is selecting a subset of individuals from a population, and sampling distributions show the distribution of sample statistics like the mean.
3) The document also discusses hypothesis testing, types of errors, significance levels, confidence intervals for estimating population parameters, and using the t-distribution to test hypotheses when the population standard deviation is unknown.
This document provides an overview of key concepts related to random variables and probability distributions. It discusses:
- Two types of random variables - discrete and continuous. Discrete variables can take countable values, continuous can be any value in an interval.
- Probability distributions for discrete random variables, which specify the probability of each possible outcome. Examples of common discrete distributions like binomial and Poisson are provided.
- Key properties and calculations for discrete distributions like expected value, variance, and the formulas for binomial and Poisson probabilities.
- Other discrete distributions like hypergeometric are introduced for situations where outcomes are not independent. Examples are provided to demonstrate calculating probabilities for each type of distribution.
Statistics and Probability-Random Variables and Probability DistributionApril Palmes
Here are the solutions to the problems:
1. a) Mean = 0.05 rotten tomatoes
b) P(x>1) = 0.03
2. a) Mean = 3.5
b) Variance = 35/12 = 2.91667
c) Standard deviation = 1.7321
3. a) Mean = $0.80
b) Variance = $2.40
4. X Probability
0 1/8
1 3/8
2 3/8
3 1/8
This document outlines key concepts related to discrete and continuous random variables including:
- Discrete random variables can take countable values while continuous can take any value in an interval.
- The probability distribution of a discrete random variable lists all possible values and their probabilities.
- Key metrics for discrete variables include the mean, which is the expected value, and standard deviation, which measures spread.
- The cumulative distribution function provides the probability that a random variable is less than or equal to a given value.
The document discusses probability distributions, which model the probabilities of outcomes in random phenomena. It covers:
- Discrete and continuous probability distributions, which model outcomes that are discrete or continuous.
- Key properties of distributions like the mean, variance, and standard deviation, which describe the central tendency and variation of outcomes.
- Specific discrete distributions like the binomial and Poisson, which model counts of successes/failures and rare events.
- The normal/Gaussian distribution as the most common continuous distribution, fully described by its mean and variance.
- Standardizing normal variables to the standard normal distribution with mean 0 and variance 1 for easier probability calculations.
The document discusses plasma proteins and their functions. It begins by explaining how plasma carries vital components like nutrients, electrolytes, and hormones throughout the body. The three main plasma protein fractions - albumin, globulins, and fibrinogen - are described. Albumin maintains fluid balance while globulins and fibrinogen aid in immune defense and blood clotting. The document then examines the specific roles and properties of important plasma proteins like immunoglobulins, complement proteins, fibrinogen, and transport proteins. It concludes by explaining how plasma proteins work with platelets to form blood clots and maintain the integrity of the circulatory system.
The respiratory system consists of the nose, pharynx, larynx, trachea, bronchi, and lungs. Its primary function is to provide oxygen to cells and remove carbon dioxide. External respiration is the exchange of gases in the lungs, while internal respiration is the exchange of gases at the cellular level. The respiratory system works with the circulatory system to deliver oxygen throughout the body and remove carbon dioxide.
This document discusses discrete probability distributions, specifically the binomial and Poisson distributions. It provides information on calculating probabilities using the binomial and Poisson probability formulas and tables. It defines key characteristics of binomial experiments and conditions for applying the binomial and Poisson distributions. Examples are given to demonstrate calculating probabilities for each distribution, including finding the mean, variance and standard deviation for binomial distributions.
The document discusses discrete and continuous random variables. It defines discrete random variables as variables that can take on countable values, like the number of heads from coin flips. Continuous random variables can take any value within a range, like height. The document explains how to calculate and interpret the mean, standard deviation, and probabilities of events for both types of random variables using examples like Apgar scores for babies and heights of young women.
The central limit theorem states that the sampling distribution of the sample mean x will be approximately normally distributed for sample sizes n greater than 30, regardless of the shape of the population distribution. Specifically, the sampling distribution of x will have a mean equal to the population mean μ and a standard deviation of σ/√n. Similarly, for a sample proportion p, the sampling distribution of p will be approximately normal for n greater than 10 and np and nq both greater than 10, with mean equal to the population proportion p and standard deviation of √(p(1-p)/n).
Probability Distributions for Discrete Variablesgetyourcheaton
This document discusses probability distributions for discrete variables. It begins by defining a probability distribution as a relative frequency distribution of all possible outcomes of an experiment. It provides examples of probability distributions for discrete variables like the binomial distribution. It discusses key aspects of probability distributions like the mean, standard deviation, and different types of distributions like binomial. It provides examples of calculating probabilities, means, and standard deviations for binomial distributions. It discusses the basic characteristics of the binomial distribution and provides an example of constructing a binomial distribution and calculating related probabilities.
This document discusses various probability distributions including the binomial, Poisson, and normal distributions. It provides definitions and formulas for calculating probabilities for each distribution. For the binomial distribution, it covers the binomial probability formula and using the binomial table. For the Poisson distribution, it discusses the Poisson probability formula and Poisson table. It also addresses calculating the mean, variance, and standard deviation for the binomial and Poisson distributions. Finally, it introduces the normal distribution as the most important continuous probability distribution.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 5: Discrete Probability Distribution
5.2 - Binomial Probability Distributions
The document provides information about discrete and continuous random variables:
- It defines discrete and continuous random variables and gives examples of each. A discrete random variable can take countable values while a continuous random variable can take any value in an interval.
- It discusses probability distributions for discrete random variables, including defining the probability distribution and giving examples of how to construct probability distributions from data in tables. It also covers concepts like mean, standard deviation, and cumulative distribution functions.
- Various examples are provided to illustrate how to calculate probabilities, means, standard deviations, and construct probability distributions and cumulative distribution functions from data about discrete random variables. Continuous random variables are also briefly introduced.
GROUP 4 IT-A.pptx ptttt ppt ppt ppt ppt ppt pptZainUlAbedin85
This document discusses discrete random variables and their probability distributions. It defines a discrete random variable as one that has a finite or countable number of possible outcomes that can be listed. It provides examples of discrete and continuous random variables. It then explains how to construct a probability distribution for a discrete random variable by listing the possible outcomes and their probabilities, ensuring the probabilities sum to 1. It also covers how to graph a discrete probability distribution, calculate the mean, variance, and standard deviation of a discrete random variable from its probability distribution.
The document provides information on discrete and continuous random variables as well as discrete probability distributions including the binomial and Poisson distributions. It defines key terms like mean, variance, standard deviation and discusses how to calculate probabilities for these distributions. Examples are provided to demonstrate calculating probabilities for the binomial and Poisson distributions.
1. The Poisson distribution describes the probability of a number of events occurring in a fixed period of time if these events happen with a known average rate and independently of the time since the last event.
2. The Poisson distribution is defined by one parameter, usually denoted by λ, which represents the expected number of events in the given interval of time or space.
3. The probability of observing x events is given by P(X=x) = (e-λ λx)/x!, where e is the base of the natural logarithms.
Probability and Statistics : Binomial Distribution notes ppt.pdfnomovi6416
This document provides an overview of several discrete probability distributions:
- The discrete uniform distribution where each value has an equal probability of 1/k.
- The binomial distribution which models the number of successes in n independent yes/no trials with probability of success p.
- The hypergeometric distribution which models sampling without replacement from a finite population.
- The Poisson distribution which models the number of rare, independent events occurring in a fixed interval of time or space with a constant average rate λ.
Formulas are given for the probability mass functions and key properties like the mean and variance of each distribution. Examples are provided to illustrate calculating probabilities and distribution parameters.
This document defines and provides examples of discrete and continuous random variables. It also introduces key concepts such as:
- Probability mass functions and probability density functions which describe the probabilities associated with different values of discrete and continuous random variables.
- Expected value, which is the average value of a random variable calculated as the sum of each possible value multiplied by its probability.
- Variance, which measures the dispersion of a random variable from its expected value and is calculated using the probability distribution.
- The binomial distribution, which models experiments with a fixed number of trials, two possible outcomes per trial, and fixed probability of success on each trial.
Probability theory discrete probability distributionsamarthpawar9890
This document provides an overview of discrete probability distributions and binomial distributions. It begins by defining random variables and describing discrete and continuous random variables. Examples are given to distinguish between the two. The key aspects of discrete probability distributions are outlined, including how to construct a distribution and calculate measures such as mean, variance, and standard deviation. Binomial experiments are defined as having two possible outcomes, a fixed number of trials, and constant probability of success. The binomial probability formula is presented and used to calculate probabilities in examples.
This document discusses various discrete probability distributions including the binomial and Poisson distributions. It provides examples and formulas for calculating probabilities using these distributions. The key points covered are:
- The binomial distribution describes the probability of successes in a fixed number of yes/no trials where the probability of success is constant. It requires the trials to be independent and have two possible outcomes.
- The Poisson distribution describes the probability of events occurring randomly in time, space or volume. It applies when the number of events is large but the probability of any one event is small.
- Formulas are provided for calculating probabilities using the binomial and Poisson distributions, including the binomial probability formula and Poisson probability formula. Tables can also be used to find binomial and
1) The document discusses concepts from sampling theory including statistical inference, random sampling, sampling distributions, testing hypotheses, errors in hypothesis testing, significance levels, confidence intervals, and the t-distribution.
2) Key points include that statistical inference allows drawing conclusions about a population from a sample, random sampling is selecting a subset of individuals from a population, and sampling distributions show the distribution of sample statistics like the mean.
3) The document also discusses hypothesis testing, types of errors, significance levels, confidence intervals for estimating population parameters, and using the t-distribution to test hypotheses when the population standard deviation is unknown.
This document provides an overview of key concepts related to random variables and probability distributions. It discusses:
- Two types of random variables - discrete and continuous. Discrete variables can take countable values, continuous can be any value in an interval.
- Probability distributions for discrete random variables, which specify the probability of each possible outcome. Examples of common discrete distributions like binomial and Poisson are provided.
- Key properties and calculations for discrete distributions like expected value, variance, and the formulas for binomial and Poisson probabilities.
- Other discrete distributions like hypergeometric are introduced for situations where outcomes are not independent. Examples are provided to demonstrate calculating probabilities for each type of distribution.
Statistics and Probability-Random Variables and Probability DistributionApril Palmes
Here are the solutions to the problems:
1. a) Mean = 0.05 rotten tomatoes
b) P(x>1) = 0.03
2. a) Mean = 3.5
b) Variance = 35/12 = 2.91667
c) Standard deviation = 1.7321
3. a) Mean = $0.80
b) Variance = $2.40
4. X Probability
0 1/8
1 3/8
2 3/8
3 1/8
This document outlines key concepts related to discrete and continuous random variables including:
- Discrete random variables can take countable values while continuous can take any value in an interval.
- The probability distribution of a discrete random variable lists all possible values and their probabilities.
- Key metrics for discrete variables include the mean, which is the expected value, and standard deviation, which measures spread.
- The cumulative distribution function provides the probability that a random variable is less than or equal to a given value.
The document discusses probability distributions, which model the probabilities of outcomes in random phenomena. It covers:
- Discrete and continuous probability distributions, which model outcomes that are discrete or continuous.
- Key properties of distributions like the mean, variance, and standard deviation, which describe the central tendency and variation of outcomes.
- Specific discrete distributions like the binomial and Poisson, which model counts of successes/failures and rare events.
- The normal/Gaussian distribution as the most common continuous distribution, fully described by its mean and variance.
- Standardizing normal variables to the standard normal distribution with mean 0 and variance 1 for easier probability calculations.
The document discusses plasma proteins and their functions. It begins by explaining how plasma carries vital components like nutrients, electrolytes, and hormones throughout the body. The three main plasma protein fractions - albumin, globulins, and fibrinogen - are described. Albumin maintains fluid balance while globulins and fibrinogen aid in immune defense and blood clotting. The document then examines the specific roles and properties of important plasma proteins like immunoglobulins, complement proteins, fibrinogen, and transport proteins. It concludes by explaining how plasma proteins work with platelets to form blood clots and maintain the integrity of the circulatory system.
The respiratory system consists of the nose, pharynx, larynx, trachea, bronchi, and lungs. Its primary function is to provide oxygen to cells and remove carbon dioxide. External respiration is the exchange of gases in the lungs, while internal respiration is the exchange of gases at the cellular level. The respiratory system works with the circulatory system to deliver oxygen throughout the body and remove carbon dioxide.
This document discusses drugs that affect the autonomic nervous system. It begins by defining the divisions of the nervous system, including the central nervous system, peripheral nervous system, somatic nervous system, and autonomic nervous system. It then focuses on the autonomic nervous system and its sympathetic and parasympathetic divisions. The rest of the document discusses the anatomy and functions of adrenergic receptors, the effects of adrenergic and adrenergic blocking drugs, and important nursing considerations for these drug classes.
The document discusses adrenergic and anti-adrenergic drugs. It describes the sympathetic nervous system which uses norepinephrine as a neurotransmitter. Adrenergic drugs can work directly on receptors, indirectly by increasing norepinephrine release, or through a mixed mechanism. Examples provided are epinephrine, phenylephrine, and ephedrine. Anti-adrenergic drugs block sympathetic effects and are divided into alpha and beta blockers such as prazosin, propranolol, and labetalol. Specific indications, mechanisms of action, and considerations for use are described for various adrenergic and anti-adrenergic drugs.
1. The document provides an overview of radiological anatomy of the chest and describes how to examine a posteroanterior chest radiograph. It identifies bones, soft tissues, trachea, lungs, diaphragm, heart and mediastinum.
2. Bronchography and contrast visualization of the esophagus are described as special studies to visualize the bronchial tree and esophagus.
3. Coronary angiography is mentioned as a method to visualize the coronary arteries and identify any narrowing or blockage.
This document discusses the difference between discrete and continuous functions. Discrete functions only have distinct, countable points and do not connect the dots, like the number of students in a class. Continuous functions have all possible points within a given interval, including decimals, like the height of students. An example graph is given with two sets of numbers that represent a discrete function, with the domain and range being the individual numbers.
This document discusses various sampling methods used in research. It defines key terms like population, element, parameter, and statistic. It also describes different sampling techniques including probability methods like random sampling, stratified sampling, and cluster sampling as well as non-probability methods like convenience sampling, judgment sampling, and snowball sampling. The document highlights important considerations for sample size and achieving high response rates.
This document discusses sampling techniques used in business research. It covers the key concepts of sampling, including probability and non-probability sampling. Probability sampling techniques discussed include simple random sampling, systematic sampling, stratified sampling, cluster sampling, and double sampling. Non-probability sampling techniques include convenience sampling, judgment sampling, and quota sampling. The document also covers how to determine appropriate sample sizes for estimating means and proportions, including calculating margins of error and confidence levels.
1. The document outlines various types of anemia including iron deficiency anemia, megaloblastic anemia caused by vitamin B12 or folate deficiencies, hemolytic anemia, and aplastic anemia.
2. It describes the development and maturation of red blood cells from stem cells in the bone marrow to reticulocytes and mature erythrocytes.
3. Treatments for anemia include oral and parenteral iron preparations, vitamin B12 and folic acid supplements, blood transfusions, immunosuppressants, and erythropoietin therapy.
This document discusses protein digestion and amino acid metabolism. It describes the three phases of protein digestion that occur in the stomach, pancreas and small intestine. Various proteases are involved in breaking proteins down into peptides and amino acids. Amino acids are then absorbed across the intestinal epithelium through active transport mechanisms. The document also discusses intracellular protein degradation through lysosomal and ubiquitin-proteasome pathways, as well as the concept of nitrogen balance and factors that influence it.
1) RNA is synthesized by RNA polymerase in a process called transcription. In eukaryotes, there are three main types of RNA polymerases that synthesize different RNAs.
2) The basic steps of transcription are initiation, elongation, and termination. In prokaryotes, transcription initiation involves the binding of RNA polymerase and sigma factor to promoter sequences.
3) Eukaryotic transcription is more complex, involving chromatin remodeling and many transcription factors that help recruit RNA polymerase to specific gene promoters. Enhancer sequences can also increase transcription initiation from distant sites on the DNA.
Here is the updated list of Top Best Ayurvedic medicine for Gas and Indigestion and those are Gas-O-Go Syp for Dyspepsia | Lavizyme Syrup for Acidity | Yumzyme Hepatoprotective Capsules etc
Histololgy of Female Reproductive System.pptxAyeshaZaid1
Dive into an in-depth exploration of the histological structure of female reproductive system with this comprehensive lecture. Presented by Dr. Ayesha Irfan, Assistant Professor of Anatomy, this presentation covers the Gross anatomy and functional histology of the female reproductive organs. Ideal for students, educators, and anyone interested in medical science, this lecture provides clear explanations, detailed diagrams, and valuable insights into female reproductive system. Enhance your knowledge and understanding of this essential aspect of human biology.
Promoting Wellbeing - Applied Social Psychology - Psychology SuperNotesPsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
TEST BANK For An Introduction to Brain and Behavior, 7th Edition by Bryan Kol...rightmanforbloodline
TEST BANK For An Introduction to Brain and Behavior, 7th Edition by Bryan Kolb, Ian Q. Whishaw, Verified Chapters 1 - 16, Complete Newest Versio
TEST BANK For An Introduction to Brain and Behavior, 7th Edition by Bryan Kolb, Ian Q. Whishaw, Verified Chapters 1 - 16, Complete Newest Version
TEST BANK For An Introduction to Brain and Behavior, 7th Edition by Bryan Kolb, Ian Q. Whishaw, Verified Chapters 1 - 16, Complete Newest Version
Adhd Medication Shortage Uk - trinexpharmacy.comreignlana06
The UK is currently facing a Adhd Medication Shortage Uk, which has left many patients and their families grappling with uncertainty and frustration. ADHD, or Attention Deficit Hyperactivity Disorder, is a chronic condition that requires consistent medication to manage effectively. This shortage has highlighted the critical role these medications play in the daily lives of those affected by ADHD. Contact : +1 (747) 209 – 3649 E-mail : sales@trinexpharmacy.com
Integrating Ayurveda into Parkinson’s Management: A Holistic ApproachAyurveda ForAll
Explore the benefits of combining Ayurveda with conventional Parkinson's treatments. Learn how a holistic approach can manage symptoms, enhance well-being, and balance body energies. Discover the steps to safely integrate Ayurvedic practices into your Parkinson’s care plan, including expert guidance on diet, herbal remedies, and lifestyle modifications.
TEST BANK For Basic and Clinical Pharmacology, 14th Edition by Bertram G. Kat...rightmanforbloodline
TEST BANK For Basic and Clinical Pharmacology, 14th Edition by Bertram G. Katzung, Verified Chapters 1 - 66, Complete Newest Version.
TEST BANK For Basic and Clinical Pharmacology, 14th Edition by Bertram G. Katzung, Verified Chapters 1 - 66, Complete Newest Version.
TEST BANK For Basic and Clinical Pharmacology, 14th Edition by Bertram G. Katzung, Verified Chapters 1 - 66, Complete Newest Version.
TEST BANK For Basic and Clinical Pharmacology, 14th Edition by Bertram G. Katzung, Verified Chapters 1 - 66, Complete Newest Version.
2. Chapter 4: Probability Distributions
Some events can be defined using random variables.
Random variables
Variables
Random
Continuous
Variables
Random
Discrete
4.2. Probability Distributions of Discrete R.V.’s:-
Examples of discrete r v.’s
•The no. of patients visiting KKUH in a week.
•The no. of times a person had a cold in last year.
Example: Consider the following discrete random
variable.
X = The number of times a person had a cold in January
1998 in Saudi Arabia.
3. Suppose we are able to count the no. of people in Saudi
Arabia for which X = x
x Frequency of x
(no. of times a person had
a cold in January 1998 in S. A.)
(no. of people who had a cold
in January 1998 in S.A.)
0 10,000,000
1
2
3
3,000,000
2,000,000
1,000,000
Total N= 16,000,000
Simple frequency table of no. of times a person had a
cold in January 1998 in Saudi Arabia.
4. Experiment: Selecting a person at random
Define the event:
(X = x) = The event that the selected person had a
cold in January 1998 x times.
In particular,
(X = 2) = The event that the selected person had a
cold in January 1998 two times.
For this experiment, there are n(Ω)= 16,000,000 equally
likely outcomes.
000
,
000
,
16
1998
.
Januay
in
colds
x
had
who
people
of
no
n
x
X
n
x
X
P
5.
x
X
P
1600000
/
x
X
n
x freq. of x
n(X=x)
0
1
2
3
10000000
3000000
2000000
1000000
0.6250
0.1875
0.1250
0.0625
Total 16000000 1.0000
Note:
16000000
Re
16000000
frequency
Frequency
lative
x
X
n
x
X
P
6.
x
X
P
x
0
1
2
3
0.6250
0.1874
0.1250
0.0625
Total 1.0000
This table is called the probability distribution of the
discrete random variable X .
Notes:
•(X=0) , (X=1) , (X=2) , (X=3) are mutually exclusive
(disjoint) events.
7. •(X=0) , (X=1) , (X=2) , (X=3) are mutually exhaustive
events
• The probability distribution of any discrete random
variable x must satisfy the following two properties:
1
0
1
x
X
P
1
2
x
X
P
x
•Using the probability distribution of a discrete r.v. we
can find the probability of any event expressed in term
of the r.v. X.
Example:
Consider the discrete r.v. X in the previous example.
8. x P(X=x)
0
1
2
3
0.6250
0.1875
0.1250
0.0625
1875
.
0
0625
.
0
1250
.
0
3
2
2
X
P
X
P
X
P
0625
.
0
3
2
X
P
X
P
3125
.
0
1250
.
0
1875
.
0
2
1
3
1
X
P
X
P
X
P
9375
.
0
1250
.
0
1875
.
0
6250
.
0
2
1
0
2
X
P
X
P
X
P
X
P
( 1 )
( 2 )
( 3 )
( 4 )
Or
2
1
2
1
2
X
P
X
P
X
P
c
8125
.
0
1875
.
0
6250
.
0
1
0
2
1
X
P
X
P
X
P
( 5 )
9.
8125
.
0
1875
.
0
6250
.
0
1
0
3
.
1
5
.
1
X
P
X
P
X
P
( 6 )
0
5
.
3
P
X
P
( 7 )
( 8 ) The probability that the selected person had at least
2 colds
1875
.
0
3
2
2
X
P
X
P
X
P
( 9 ) The probability that the selected person had at most
2 colds
9375
.
0
2
X
P
( 10 ) The probability that the selected person had more
than 2 colds
0625
.
0
3
2
X
P
X
P
10. ( 11 ) The probability that the selected person had less
than 2 colds
8125
.
0
1
0
2
X
P
X
P
X
P
Graphical Presentation:
The probability distribution of a discrete r. v. X can be
graphically presented as follows
x P(X=x)
0
1
2
3
0.6250
0.1875
0.1250
0.0625
11. Population Mean of a Discrete Random
The mean of a discrete random variable X is denoted by
µ and defined by:
x
x
X
P
x
[mean = expected value]
Example: We wish to calculate the mean µ of the
discrete r. v. X in the previous example.
00
.
1
x
X
P
625
.
0
x
X
xP
x P(X=x) xP(X=x)
0
1
2
3
0.6250
0.1875
0.1250
0.0625
0.0
0.1875
0.2500
0.1875
Total
625
.
0
0625
.
0
3
125
.
0
2
1875
.
0
1
625
.
0
0
x
x
X
xP
12. Cumulative Distributions:
The cumulative distribution of a discrete r. v. x is
defined by
x
a
a
X
P
x
X
P
Example: The cumulative distribution of X is the
previous example is:
x
X
P
0
0
X
P
X
P
1
0
1
X
P
X
P
X
P
2
1
0
2
X
P
X
P
X
P
X
P
3
0
3
X
P
X
P
X
P
x
0
1
2
3
0.6250
0.8125
0.9375
1.0000
13. Binomial Distribution:
• It is discrete distribution.
• It is used to model an experiment for which:
1. The experiment has trials.
2. Two possible outcomes for each trial :
S= success and F= failure
3. (boy or girl, Saudi or non-Saudi,…)
4. The probability of success: is constant for each
trial.
5. The trials are independent; that is the outcome of
one trial has no effect on the outcome of any other
trial
The discrete r. v.
X = The number of successes in the n trials has a
binomial distribution with parameter n and , and we
write
,
~ n
Binomial
X
14. The probability distribution of X is given by:
otherwise
n
x
for
x
n
x
X
P
x
n
x
0
,
,
2
,
1
,
0
1
!
!
!
x
n
x
n
x
n
where
15.
x
X
P
n
n
n
1
1
0
0
0
1
1
1
1
n
n
2
2
1
2
n
n
2
1
1
1
n
n
n
n
n
n
n
0
1
We can write the probability distribution of X is a table
as follows.
x
0
1
2
: :
n 1
n
Total 1
16. Result:
If X~ Binomial (n , π ) , then
•The mean: (expected value)
•The variance:
n
1
2
n
Example: 4.2 (p.106)
Suppose that the probability that a Saudi man has high
blood pressure is 0.15. If we randomly select 6 Saudi
men, find the probability distribution of the number of
men out of 6 with high blood pressure. Also, find the
expected number of men with high blood pressure.
17. Solution:
X = The number of men with high blood pressure in 6
men.
S = Success: The man has high blood pressure
F = failure: The man does not have high blood pressure.
•Probability of success P(S) = π = 0.15
•no. of trials n=6
X ~ Binomial (6, 0.16)
6
85
.
0
1
15
.
0
n
The probability distribution of X is:
otherwise
x
x
x
X
P
x
x
;
0
6
,
5
,
4
,
3
,
2
,
1
,
0
;
85
.
0
15
.
0
6 6
20. Poisson Distribution:
• It is discrete distribution.
• The discrete r. v. X is said to have a Poisson
distribution with parameter (average) if the
probability distribution of X is given by
otherwise
x
for
x
e
x
X
P
x
;
0
,
3
,
2
,
1
,
0
;
!
where e = 2.71828 (the natural number ).
x
e
x ln
We write:
X ~ Poisson ( λ )
• The mean (average) of Poisson () is : μ =
λ
• The variance is:
2
21. •The Poisson distribution is used to model a discrete r.
v. which is a count of how many times a specified
random event occurred in an interval of time or space.
Example:
•No. of patients in a waiting room in an hours.
•No. of serious injuries in a particular factory in a
month.
•No. of calls received by a telephone operator in a day.
•No. of rates in each house in a particular city.
Note:
is the average (mean) of the distribution.
If X = The number of calls received in a month and
X ~ Poisson ()
22. then:
(i) Y = The no. calls received in a year.
Y ~ Poisson (*), where *=12
Y ~ Poisson (12)
(ii)W = The no. calls received in a day.
W ~ Poisson (*), where *=/30
W ~ Poisson (/30)
Example:
Suppose that the number of snake bites cases seen at
KKUH in a year has a Poisson distribution with average
6 bite cases.
1- What is the probability that in a year:
(i) The no. of snake bite cases will be 7?
(ii) The no. of snake bite cases will be less than 2?
23. 2- What is the probability that in 2 years there will be 10
bite cases?
3- What is the probability that in a month there will be
no snake bite cases?
Solution:
(1) X = no. of snake bite cases in a year.
X ~ Poisson (6) (=6)
,
2
,
1
,
0
;
!
6
6
x
x
e
x
X
P
x
13768
.
0
!
7
6
)
7
7
6
e
X
P
01735
.
0
!
1
6
!
0
6
1
0
2
1
6
0
6
e
e
X
P
X
P
X
P
(i)
(ii)
24. Y = no of snake bite cases in 2 years
Y ~ Poisson(12) )
12
6
2
2
( *
2
,
1
,
0
:
!
12
12
y
y
e
y
Y
P
y
1048
.
0
10
12
10
10
12
e
Y
P
3- W = no. of snake bite cases in a month.
W ~ Poisson (0.5) 5
.
0
12
6
12
*
*
2
,
1
,
0
:
!
5
.
5
.
w
w
e
w
W
P
w
6065
.
0
!
0
5
.
0
0
0
5
.
0
e
W
P