1) The document discusses probability concepts and their application to archaeology, including binomial probability, which can help evaluate whether differences observed between artifact samples are statistically significant or could be due to chance.
2) An example examines the likelihood of finding no ceramic wasters in a sample of 15 sherds from a site, given that wasters typically make up 5% of samples from ceramic workshops.
3) Cumulative probability distributions are useful when interested in the probability of outcomes more extreme than what was directly observed, such as fewer burials of a certain type than expected by chance.
1. The document discusses probability concepts like binomial distributions and using Bayes' theorem in archaeology. It provides examples of estimating the probability of outcomes based on artifact samples.
2. One example examines the probability of missing ceramic "wasters" in a sample of 15 sherds, finding over a 46% chance of obtaining that result even from a workshop.
3. Cumulative density functions are useful for assessing the likelihood of observations, not just single outcomes, by considering more extreme probabilities. An example evaluates burial data this way.
This document discusses key concepts in probability and how they can be applied in archaeology. It begins by explaining the frequentist and Bayesian approaches to probability. The basic concepts of probability, independent and conditional probability, and Bayes' Theorem are then defined. Examples are provided to demonstrate how binomial probability, probability density functions, and cumulative density functions can help archaeologists evaluate the significance of artifact samples and absence of types. Specifically, these statistical tools allow researchers to assess how likely it is their results are due to chance rather than reflecting real patterns in the archaeological record.
The document discusses key concepts in probability and their application to archaeological data analysis. It explains that probability can be assessed from both frequentist and Bayesian perspectives. The frequentist view assesses probabilities as objective frequencies of outcomes, while the Bayesian view incorporates prior knowledge. Several probability concepts are defined, including discrete vs. continuous probabilities and independent vs. conditional probabilities. The binomial theorem is introduced for calculating probabilities of outcomes from repeated trials. The document demonstrates how these probability concepts can help archaeologists evaluate sample sizes, absence of artifact types, and differences between sites while accounting for chance.
This document discusses probability theories and formulas. It defines probability as a branch of mathematics dealing with random phenomena and introduces key concepts like experiments, sample spaces, events, and equally likely probabilities. It provides examples of experiments like coin tosses, dice rolls, and drawing balls from an urn. The document also covers basic probability formulas like addition rule, complementary events, disjoint and independent events. It gives examples of calculating probabilities and introduces the conditional probability formula.
This document provides an overview of probability and how it relates to statistics. It defines probability as a method for quantifying the likelihood of outcomes. Probability is measured as a ratio of the number of desired outcomes to the total number of possible outcomes. For outcomes to have a known probability, they must be selected through a random process. The normal distribution is discussed as it relates to probability, with common probabilities and areas under the normal curve defined. The document shows how to calculate probabilities for raw scores on a normal distribution using z-scores. It also demonstrates finding probabilities for ranges of scores and finding z-scores from known proportions.
This document discusses probability concepts for data science. It begins by defining probability and statistics, then covers key terms like events, random variables, empirical and theoretical probability, joint and conditional probability, probability distributions, and the central limit theorem. Examples are provided to illustrate concepts like independent and mutually exclusive events. Genetic algorithms are also introduced as a case study, outlining the phases of initializing a population, fitness functions, selection, crossover and mutation.
This document provides an overview of probability concepts including:
- Probability is a numerical measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
- An experiment generates outcomes that make up the sample space. Events are collections of outcomes.
- Simple events have a defined probability based on being equally likely. The probability of an event is the sum of probabilities of the simple events it contains.
- Rules like the multiplication rule for independent events and additive rule for unions allow calculating probabilities of composite events.
- Complement and conditional probabilities relate the probabilities of events. Independent events do not influence each other's probabilities.
This document provides an overview of key probability concepts including:
(1) Definitions of random experiments, sample spaces, events, and probability;
(2) The addition and multiplication theorems and conditional probability;
(3) Mathematical expectation and probability distributions including the binomial, Poisson, and normal distributions. Examples are provided to illustrate key terminology and formulas.
1. The document discusses probability concepts like binomial distributions and using Bayes' theorem in archaeology. It provides examples of estimating the probability of outcomes based on artifact samples.
2. One example examines the probability of missing ceramic "wasters" in a sample of 15 sherds, finding over a 46% chance of obtaining that result even from a workshop.
3. Cumulative density functions are useful for assessing the likelihood of observations, not just single outcomes, by considering more extreme probabilities. An example evaluates burial data this way.
This document discusses key concepts in probability and how they can be applied in archaeology. It begins by explaining the frequentist and Bayesian approaches to probability. The basic concepts of probability, independent and conditional probability, and Bayes' Theorem are then defined. Examples are provided to demonstrate how binomial probability, probability density functions, and cumulative density functions can help archaeologists evaluate the significance of artifact samples and absence of types. Specifically, these statistical tools allow researchers to assess how likely it is their results are due to chance rather than reflecting real patterns in the archaeological record.
The document discusses key concepts in probability and their application to archaeological data analysis. It explains that probability can be assessed from both frequentist and Bayesian perspectives. The frequentist view assesses probabilities as objective frequencies of outcomes, while the Bayesian view incorporates prior knowledge. Several probability concepts are defined, including discrete vs. continuous probabilities and independent vs. conditional probabilities. The binomial theorem is introduced for calculating probabilities of outcomes from repeated trials. The document demonstrates how these probability concepts can help archaeologists evaluate sample sizes, absence of artifact types, and differences between sites while accounting for chance.
This document discusses probability theories and formulas. It defines probability as a branch of mathematics dealing with random phenomena and introduces key concepts like experiments, sample spaces, events, and equally likely probabilities. It provides examples of experiments like coin tosses, dice rolls, and drawing balls from an urn. The document also covers basic probability formulas like addition rule, complementary events, disjoint and independent events. It gives examples of calculating probabilities and introduces the conditional probability formula.
This document provides an overview of probability and how it relates to statistics. It defines probability as a method for quantifying the likelihood of outcomes. Probability is measured as a ratio of the number of desired outcomes to the total number of possible outcomes. For outcomes to have a known probability, they must be selected through a random process. The normal distribution is discussed as it relates to probability, with common probabilities and areas under the normal curve defined. The document shows how to calculate probabilities for raw scores on a normal distribution using z-scores. It also demonstrates finding probabilities for ranges of scores and finding z-scores from known proportions.
This document discusses probability concepts for data science. It begins by defining probability and statistics, then covers key terms like events, random variables, empirical and theoretical probability, joint and conditional probability, probability distributions, and the central limit theorem. Examples are provided to illustrate concepts like independent and mutually exclusive events. Genetic algorithms are also introduced as a case study, outlining the phases of initializing a population, fitness functions, selection, crossover and mutation.
This document provides an overview of probability concepts including:
- Probability is a numerical measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
- An experiment generates outcomes that make up the sample space. Events are collections of outcomes.
- Simple events have a defined probability based on being equally likely. The probability of an event is the sum of probabilities of the simple events it contains.
- Rules like the multiplication rule for independent events and additive rule for unions allow calculating probabilities of composite events.
- Complement and conditional probabilities relate the probabilities of events. Independent events do not influence each other's probabilities.
This document provides an overview of key probability concepts including:
(1) Definitions of random experiments, sample spaces, events, and probability;
(2) The addition and multiplication theorems and conditional probability;
(3) Mathematical expectation and probability distributions including the binomial, Poisson, and normal distributions. Examples are provided to illustrate key terminology and formulas.
This document discusses probability and related concepts. It defines probability as the study of uncertainty and notes its uses in fields like mathematics, science, and medicine. Key terms are introduced, including random experiments, trials, events, and elementary events. Experimental probability is defined based on the number of trials and outcomes. Examples are provided to demonstrate calculating probabilities and the relationship that the probabilities of all elementary events sum to 1.
Basic probability concepts are introduced including experiments, outcomes, events, sample space, elementary events, simple and joint probabilities. Key terms like mutually exclusive, independent and dependent events are defined. Formulas for calculating probabilities of simple, joint, union and intersection of events are provided. Examples of tossing coins, rolling dice and selecting items from sets are used to illustrate concepts. Probability relationships like complement, addition rule for mutually exclusive events and general addition rule are explained using Venn diagrams and examples.
1. Probability is the study of randomness and uncertainty of outcomes from experiments or processes. It allows us to make statements about the likelihood of events occurring.
2. Events are outcomes or sets of outcomes from random experiments. The probability of an event is calculated based on the number of outcomes in the event compared to the total number of possible outcomes.
3. Conditional probability is the likelihood of one event occurring given that another event has occurred. It is calculated as the probability of both events occurring divided by the probability of the first event. Conditional probabilities are useful for problems involving dependent events.
The document discusses key concepts in probability theory, including sample space, events, and terminology. It provides examples of sample spaces and events for experiments like rolling dice or selecting cards from a deck. The three main approaches to assigning probabilities - classical, relative frequency, and subjective - are also outlined. The section concludes by introducing the addition rule for probabilities of unions of events.
This document provides an introduction to probability. It defines key probability terms like certain, likely, equally likely, unlikely, and impossible. It explains how to calculate the probability of an event using the formula: Probability (P) = Number of favorable outcomes / Total number of possible outcomes. It provides examples of calculating probabilities for events like drawing cards from a deck or numbers on a clock. It concludes with several word problems asking the reader to calculate probabilities based on the information provided.
This document provides an introduction to probability and statistics concepts over 2 weeks. It covers basic probability topics like sample spaces, events, probability definitions and axioms. Conditional probability and the multiplication rule for conditional probability are explained. Bayes' theorem relating prior, likelihood and posterior probabilities is introduced. Examples on probability calculations for coin tosses, dice rolls and medical testing are provided. Key terms around experimental units, populations, descriptive and inferential statistics are also defined.
- Cosmology relies heavily on statistics and probability to analyze astronomical data and test theories of the universe.
- Bayesian probability provides a rigorous way to assign probabilities to hypotheses based on prior knowledge and new data, and update beliefs.
- The universe appears "fine tuned" for life with parameter values that allow complexity; Bayesian reasoning can help assess if these are surprising coincidences.
- The concordance model of cosmology posits that initial fluctuations in the early universe formed a Gaussian random field, but some anomalies in cosmic microwave background data could indicate "weirdness" beyond this simple picture.
Basic statistics for algorithmic tradingQuantInsti
In this presentation we try to understand the core basics of statistics and its application in algorithmic trading.
We start by defining what statistics is. Collecting data is the root of statistics. We need data to analyse and take quantitative decisions.
While analyzing, there are certain parameters for statistics, this branches statistics into two - descriptive statistics & inferential statistics.
This data that we have collected can be classified into uni-variate and bi-variate. It also tries to explain the fundamental difference.
Going Further we also cover topics like regression line, Coefficient of Determination, Homoscedasticity and Heteroscedasticity.
In this way the presentation look at various aspects of statistics which are used for algorithmic trading.
To learn the advanced applications of statistics for HFT & Quantitative Trading connect with us one our website: www.quantinsti.com.
- Mathematics originated in ancient Egypt and Babylon, where early concepts like counting, arithmetic operations, and basic geometry were developed.
- In ancient Greece, mathematics advanced significantly with figures like Pythagoras, Euclid, Archimedes, and others who established foundations of geometry, number theory, and began developing proofs and formal logic.
- Over centuries, mathematicians solved important problems like finding formulas for quadratic and cubic equations, establishing that some problems like "squaring the circle" are impossible to solve with compass and straightedge, and developing calculus to solve problems involving change and rates of change.
The document discusses different concepts in statistics and probability including sampling, random variables, probability distributions, and computing probabilities for random variables. It provides examples of discrete and continuous random variables, as well as examples of constructing probability distributions and calculating probabilities corresponding to random variables. The document also briefly covers topics like conditional probability.
This document presents algorithmic puzzles and their solutions. It discusses puzzles involving counterfeit coins, uneven water pitchers, strong eggs on tiny floors, and people arranged in a circle. For each puzzle, it provides the problem description, an analysis or solution approach, and sometimes additional discussion. The document is a presentation on algorithmic puzzles given by Amrinder Arora, including their contact information.
This document provides an overview of probability concepts including:
- Definitions of random experiments, sample spaces, events, and axiomatic probability
- Examples of sample spaces for common experiments
- The basic principle of counting and examples of permutations and combinations
- Formulas for classical probability, permutations, and combinations
- Examples of calculating probabilities and counting outcomes for experiments
Probability theory provides the foundation for statistical inference and allows conclusions to be drawn about populations based on sample data. There are two main categories of probability - objective and subjective. Objective probability includes classical and relative frequency probabilities. Probability distributions describe the possible outcomes of random variables and include discrete distributions like the binomial. Probability theory is used in understanding distributions, sampling, estimation, hypothesis testing, and advanced statistical analysis.
Lessons from experience: engaging with quantum crackpotsRichard Gill
This document summarizes Richard Gill's discussion of engaging with proponents of alternative interpretations of quantum mechanics, or "quantum crackpots". Gill discusses how interacting with quantum crackpots has led to productive outcomes in his own work, such as resolving experimental loopholes in Bell test experiments and publishing collaborative papers. However, Gill also notes that quantum crackpots often lack understanding of statistics and mathematics. Overall, Gill advocates respectful engagement with alternative viewpoints as a way to further scientific progress, while also acknowledging the challenges in communication across disciplines.
This document provides an overview of key concepts in probability, including experiment, event, sample space, unions and intersections of events, mutually exclusive events, and methods of assigning probabilities. It discusses experiments, events, and sample spaces. It defines union and intersection of sets. It covers classical, relative frequency, and subjective probabilities. It also discusses rules for counting sample points, including multiplication, permutation, and combination. Examples are provided to illustrate calculating probabilities.
Fisher conducted an experiment to determine if Muriel Bristol could distinguish between tea prepared with milk first versus tea first. He formulated the null hypothesis that Bristol was guessing randomly, and the alternative hypothesis that she could tell the difference. Bristol correctly identified the preparation method for 8 cups of tea. The probability of this occurring by chance under the null hypothesis is 3.5%, which is lower than Fisher's threshold of 14% to reject the null hypothesis. Therefore, Fisher rejected the idea that Bristol was guessing randomly, and concluded that she could distinguish between milk-first and tea-first tea preparation.
This document provides an introduction to simple probability concepts including:
- Definitions of outcomes, favorable outcomes, and theoretical probability
- Examples of calculating probability for single-step experiments like rolling a die
- Representing two-step experiments using ordered pairs and calculating probabilities using tables
- The relationship between experimental probability from trials and theoretical probability as the number of trials increases
The document provides an overview of elementary probability concepts including:
- Defining probability as the chance of an event occurring and explaining common probability notions.
- Introducing key probability terms like sample space, events, outcomes, and complementary/intersection of events.
- Explaining counting rules like the addition rule, multiplication rule, and how to calculate permutations and combinations.
- Outlining different approaches to defining probability including classical, subjective, axiomatic, and frequency-based definitions.
- Detailing several probability rules like calculating the probability of a union of events and applying the addition rule to non-mutually exclusive events.
The document provides an overview of elementary probability concepts including:
- Defining probability as the chance of an event occurring and explaining common probability notions.
- Introducing key probability terms like sample space, events, outcomes, and complementary/intersection of events.
- Explaining counting rules like the addition rule, multiplication rule, and how to calculate permutations and combinations.
- Outlining different approaches to defining probability including classical, subjective, axiomatic, and frequency-based definitions.
- Detailing several probability rules like calculating the probability of a union of events and applying the addition rule to non-mutually exclusive events.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
This document discusses probability and related concepts. It defines probability as the study of uncertainty and notes its uses in fields like mathematics, science, and medicine. Key terms are introduced, including random experiments, trials, events, and elementary events. Experimental probability is defined based on the number of trials and outcomes. Examples are provided to demonstrate calculating probabilities and the relationship that the probabilities of all elementary events sum to 1.
Basic probability concepts are introduced including experiments, outcomes, events, sample space, elementary events, simple and joint probabilities. Key terms like mutually exclusive, independent and dependent events are defined. Formulas for calculating probabilities of simple, joint, union and intersection of events are provided. Examples of tossing coins, rolling dice and selecting items from sets are used to illustrate concepts. Probability relationships like complement, addition rule for mutually exclusive events and general addition rule are explained using Venn diagrams and examples.
1. Probability is the study of randomness and uncertainty of outcomes from experiments or processes. It allows us to make statements about the likelihood of events occurring.
2. Events are outcomes or sets of outcomes from random experiments. The probability of an event is calculated based on the number of outcomes in the event compared to the total number of possible outcomes.
3. Conditional probability is the likelihood of one event occurring given that another event has occurred. It is calculated as the probability of both events occurring divided by the probability of the first event. Conditional probabilities are useful for problems involving dependent events.
The document discusses key concepts in probability theory, including sample space, events, and terminology. It provides examples of sample spaces and events for experiments like rolling dice or selecting cards from a deck. The three main approaches to assigning probabilities - classical, relative frequency, and subjective - are also outlined. The section concludes by introducing the addition rule for probabilities of unions of events.
This document provides an introduction to probability. It defines key probability terms like certain, likely, equally likely, unlikely, and impossible. It explains how to calculate the probability of an event using the formula: Probability (P) = Number of favorable outcomes / Total number of possible outcomes. It provides examples of calculating probabilities for events like drawing cards from a deck or numbers on a clock. It concludes with several word problems asking the reader to calculate probabilities based on the information provided.
This document provides an introduction to probability and statistics concepts over 2 weeks. It covers basic probability topics like sample spaces, events, probability definitions and axioms. Conditional probability and the multiplication rule for conditional probability are explained. Bayes' theorem relating prior, likelihood and posterior probabilities is introduced. Examples on probability calculations for coin tosses, dice rolls and medical testing are provided. Key terms around experimental units, populations, descriptive and inferential statistics are also defined.
- Cosmology relies heavily on statistics and probability to analyze astronomical data and test theories of the universe.
- Bayesian probability provides a rigorous way to assign probabilities to hypotheses based on prior knowledge and new data, and update beliefs.
- The universe appears "fine tuned" for life with parameter values that allow complexity; Bayesian reasoning can help assess if these are surprising coincidences.
- The concordance model of cosmology posits that initial fluctuations in the early universe formed a Gaussian random field, but some anomalies in cosmic microwave background data could indicate "weirdness" beyond this simple picture.
Basic statistics for algorithmic tradingQuantInsti
In this presentation we try to understand the core basics of statistics and its application in algorithmic trading.
We start by defining what statistics is. Collecting data is the root of statistics. We need data to analyse and take quantitative decisions.
While analyzing, there are certain parameters for statistics, this branches statistics into two - descriptive statistics & inferential statistics.
This data that we have collected can be classified into uni-variate and bi-variate. It also tries to explain the fundamental difference.
Going Further we also cover topics like regression line, Coefficient of Determination, Homoscedasticity and Heteroscedasticity.
In this way the presentation look at various aspects of statistics which are used for algorithmic trading.
To learn the advanced applications of statistics for HFT & Quantitative Trading connect with us one our website: www.quantinsti.com.
- Mathematics originated in ancient Egypt and Babylon, where early concepts like counting, arithmetic operations, and basic geometry were developed.
- In ancient Greece, mathematics advanced significantly with figures like Pythagoras, Euclid, Archimedes, and others who established foundations of geometry, number theory, and began developing proofs and formal logic.
- Over centuries, mathematicians solved important problems like finding formulas for quadratic and cubic equations, establishing that some problems like "squaring the circle" are impossible to solve with compass and straightedge, and developing calculus to solve problems involving change and rates of change.
The document discusses different concepts in statistics and probability including sampling, random variables, probability distributions, and computing probabilities for random variables. It provides examples of discrete and continuous random variables, as well as examples of constructing probability distributions and calculating probabilities corresponding to random variables. The document also briefly covers topics like conditional probability.
This document presents algorithmic puzzles and their solutions. It discusses puzzles involving counterfeit coins, uneven water pitchers, strong eggs on tiny floors, and people arranged in a circle. For each puzzle, it provides the problem description, an analysis or solution approach, and sometimes additional discussion. The document is a presentation on algorithmic puzzles given by Amrinder Arora, including their contact information.
This document provides an overview of probability concepts including:
- Definitions of random experiments, sample spaces, events, and axiomatic probability
- Examples of sample spaces for common experiments
- The basic principle of counting and examples of permutations and combinations
- Formulas for classical probability, permutations, and combinations
- Examples of calculating probabilities and counting outcomes for experiments
Probability theory provides the foundation for statistical inference and allows conclusions to be drawn about populations based on sample data. There are two main categories of probability - objective and subjective. Objective probability includes classical and relative frequency probabilities. Probability distributions describe the possible outcomes of random variables and include discrete distributions like the binomial. Probability theory is used in understanding distributions, sampling, estimation, hypothesis testing, and advanced statistical analysis.
Lessons from experience: engaging with quantum crackpotsRichard Gill
This document summarizes Richard Gill's discussion of engaging with proponents of alternative interpretations of quantum mechanics, or "quantum crackpots". Gill discusses how interacting with quantum crackpots has led to productive outcomes in his own work, such as resolving experimental loopholes in Bell test experiments and publishing collaborative papers. However, Gill also notes that quantum crackpots often lack understanding of statistics and mathematics. Overall, Gill advocates respectful engagement with alternative viewpoints as a way to further scientific progress, while also acknowledging the challenges in communication across disciplines.
This document provides an overview of key concepts in probability, including experiment, event, sample space, unions and intersections of events, mutually exclusive events, and methods of assigning probabilities. It discusses experiments, events, and sample spaces. It defines union and intersection of sets. It covers classical, relative frequency, and subjective probabilities. It also discusses rules for counting sample points, including multiplication, permutation, and combination. Examples are provided to illustrate calculating probabilities.
Fisher conducted an experiment to determine if Muriel Bristol could distinguish between tea prepared with milk first versus tea first. He formulated the null hypothesis that Bristol was guessing randomly, and the alternative hypothesis that she could tell the difference. Bristol correctly identified the preparation method for 8 cups of tea. The probability of this occurring by chance under the null hypothesis is 3.5%, which is lower than Fisher's threshold of 14% to reject the null hypothesis. Therefore, Fisher rejected the idea that Bristol was guessing randomly, and concluded that she could distinguish between milk-first and tea-first tea preparation.
This document provides an introduction to simple probability concepts including:
- Definitions of outcomes, favorable outcomes, and theoretical probability
- Examples of calculating probability for single-step experiments like rolling a die
- Representing two-step experiments using ordered pairs and calculating probabilities using tables
- The relationship between experimental probability from trials and theoretical probability as the number of trials increases
The document provides an overview of elementary probability concepts including:
- Defining probability as the chance of an event occurring and explaining common probability notions.
- Introducing key probability terms like sample space, events, outcomes, and complementary/intersection of events.
- Explaining counting rules like the addition rule, multiplication rule, and how to calculate permutations and combinations.
- Outlining different approaches to defining probability including classical, subjective, axiomatic, and frequency-based definitions.
- Detailing several probability rules like calculating the probability of a union of events and applying the addition rule to non-mutually exclusive events.
The document provides an overview of elementary probability concepts including:
- Defining probability as the chance of an event occurring and explaining common probability notions.
- Introducing key probability terms like sample space, events, outcomes, and complementary/intersection of events.
- Explaining counting rules like the addition rule, multiplication rule, and how to calculate permutations and combinations.
- Outlining different approaches to defining probability including classical, subjective, axiomatic, and frequency-based definitions.
- Detailing several probability rules like calculating the probability of a union of events and applying the addition rule to non-mutually exclusive events.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
Preparation and standardization of the following : Tonic, Bleaches, Dentifrices and Mouth washes & Tooth Pastes, Cosmetics for Nails.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Assessment and Planning in Educational technology.pptxKavitha Krishnan
In an education system, it is understood that assessment is only for the students, but on the other hand, the Assessment of teachers is also an important aspect of the education system that ensures teachers are providing high-quality instruction to students. The assessment process can be used to provide feedback and support for professional development, to inform decisions about teacher retention or promotion, or to evaluate teacher effectiveness for accountability purposes.
2. Questions
• what is a good general size for artifact
samples?
• what proportion of populations of interest
should we be attempting to sample?
• how do we evaluate the absence of an
artifact type in our collections?
3. “frequentist” approach
• probability should be assessed in purely
objective terms
• no room for subjectivity on the part of
individual researchers
• knowledge about probabilities comes from
the relative frequency of a large number of
trials
– this is a good model for coin tossing
– not so useful for archaeology, where many of
the events that interest us are unique…
4. Bayesian approach
• Bayes Theorem
– Thomas Bayes
– 18th
century English clergyman
• concerned with integrating “prior knowledge” into
calculations of probability
• problematic for frequentists
– prior knowledge = bias, subjectivity…
5. basic concepts
• probability of event = p
0 <= p <= 1
0 = certain non-occurrence
1 = certain occurrence
• .5 = even odds
• .1 = 1 chance out of 10
6. • if A and B are mutually exclusive events:
P(A or B) = P(A) + P(B)
ex., die roll: P(1 or 6) = 1/6 + 1/6 = .33
• possibility set:
sum of all possible outcomes
~A = anything other than A
P(A or ~A) = P(A) + P(~A) = 1
basic concepts (cont.)
7. • discrete vs. continuous probabilities
• discrete
– finite number of outcomes
• continuous
– outcomes vary along continuous scale
basic concepts (cont.)
10. independent events
• one event has no influence on the outcome
of another event
• if events A & B are independent
then P(A&B) = P(A)*P(B)
• if P(A&B) = P(A)*P(B)
then events A & B are independent
• coin flipping
if P(H) = P(T) = .5 then
P(HTHTH) = P(HHHHH) =
.5*.5*.5*.5*.5 = .55
= .03
11. • if you are flipping a coin and it has already
come up heads 6 times in a row, what are
the odds of an 7th
head?
.5
• note that P(10H) < > P(4H,6T)
– lots of ways to achieve the 2nd
result (therefore
much more probable)
12. • mutually exclusive events are not
independent
• rather, the most dependent kinds of events
– if not heads, then tails
– joint probability of 2 mutually exclusive events
is 0
• P(A&B)=0
13. conditional probability
• concern the odds of one event occurring,
given that another event has occurred
• P(A|B)=Prob of A, given B
14. e.g.
• consider a temporally ambiguous, but
generally late, pottery type
• the probability that an actual example is
“late” increases if found with other types of
pottery that are unambiguously late…
• P = probability that the specimen is late:
isolated: P(Ta
) = .7
w/ late pottery (Tb): P(Ta
|Tb
) = .9
w/ early pottery (Tc): P(Ta
|Tc
) = .3
15. • P(B|A) = P(A&B)/P(A)
• if A and B are independent, then
P(B|A) = P(A)*P(B)/P(A)
P(B|A) = P(B)
conditional probability (cont.)
16. Bayes Theorem
• can be derived from the basic equation for
conditional probabilities
( ) ( ) ( )
( ) ( ) ( ) ( )BAPBPBAPBP
BAPBP
ABP
|~~|
|
|
+
=
17. application
• archaeological data about ceramic design
– bowls and jars, decorated and undecorated
• previous excavations show:
– 75% of assemblage are bowls, 25% jars
– of the bowls, about 50% are decorated
– of the jars, only about 20% are decorated
• we have a decorated sherd fragment, but it’s too
small to determine its form…
• what is the probability that it comes from a bowl?
18. • can solve for P(B|A)
• events:??
• events: B = “bowlness”; A = “decoratedness”
• P(B)=??; P(A|B)=??
• P(B)=.75; P(A|B)=.50
• P(~B)=.25; P(A|~B)=.20
• P(B|A)=.75*.50 / ((.75*50)+(.25*.20))
• P(B|A)=.88
bowl jar
dec. ?? 50% of bowls
20% of jars
undec. 50% of bowls
80% of jars
75% 25%
( ) ( ) ( )
( ) ( ) ( ) ( )BAPBPBAPBP
BAPBP
ABP
|~~|
|
|
+
=
19. Binomial theorem
• P(n,k,p)
– probability of k successes in n trials
where the probability of success on any one
trial is p
– “success” = some specific event or outcome
– k specified outcomes
– n trials
– p probability of the specified outcome in 1 trial
20. ( ) ( ) ( ) knk
ppknCpknP
−
−= 1,,,
( )
( )!!
!
,
knk
n
knC
−
=
where
n! = n*(n-1)*(n-2)…*1 (where n is an integer)
0!=1
21. binomial distribution
• binomial theorem describes a theoretical
distribution that can be plotted in two
different ways:
– probability density function (PDF)
– cumulative density function (CDF)
22. probability density function (PDF)
• summarizes how odds/probabilities are
distributed among the events that can arise
from a series of trials
23. ex: coin toss
• we toss a coin three times, defining the
outcome head as a “success”…
• what are the possible outcomes?
• how do we calculate their probabilities?
24. coin toss (cont.)
• how do we assign values to
P(n,k,p)?
• 3 trials; n = 3
• even odds of success; p=.5
• P(3,k,.5)
• there are 4 possible values for ‘k’,
and we want to calculate P for
each of them
k
0 TTT
1 HTT (THT,TTH)
2 HHT (HTH, THH)
3 HHH
“probability of k successes in n trials
where the probability of success on any one trial is p”
26. practical applications
• how do we interpret the absence of key
types in artifact samples??
• does sample size matter??
• does anything else matter??
27. 1. we are interested in ceramic production in
southern Utah
2. we have surface collections from a
number of sites
are any of them ceramic workshops??
3. evidence: ceramic “wasters”
ethnoarchaeological data suggests that
wasters tend to make up about 5% of samples
at ceramic workshops
example
28. • one of our sites 15 sherds, none
identified as wasters…
• so, our evidence seems to suggest that this
site is not a workshop
• how strong is our conclusion??
29. • reverse the logic: assume that it is a ceramic
workshop
• new question:
– how likely is it to have missed collecting wasters in a
sample of 15 sherds from a real ceramic workshop??
• P(n,k,p)
[n trials, k successes, p prob. of success on 1 trial]
• P(15,0,.05)
[we may want to look at other values of k…]
31. • how large a sample do you need before you
can place some reasonable confidence in the
idea that no wasters = no workshop?
• how could we find out??
• we could plot P(n,0,.05) against different
values of n…
34. so, how big should samples be?
• depends on your research goals & interests
• need big samples to study rare items…
• “rules of thumb” are usually misguided (ex.
“200 pollen grains is a valid sample”)
• in general, sheer sample size is more
important that the actual proportion
• large samples that constitute a very small
proportion of a population may be highly
useful for inferential purposes
35. • the plots we have been using are probability
density functions (PDF)
• cumulative density functions (CDF) have a
special purpose
• example based on mortuary data…
36. Site 1
• 800 graves
• 160 exhibit body position and grave goods that mark
members of a distinct ethnicity (group A)
• relative frequency of 0.2
Site 2
• badly damaged; only 50 graves excavated
• 6 exhibit “group A” characteristics
• relative frequency of 0.12
Pre-Dynastic cemeteries in Upper Egypt
37. • expressed as a proportion, Site 1 has around
twice as many burials of individuals from
“group A” as Site 2
• how seriously should we take this
observation as evidence about social
differences between underlying
populations?
38. • assume for the moment that there is no
difference between these societies—they
represent samples from the same underlying
population
• how likely would it be to collect our Site 2
sample from this underlying population?
• we could use data merged from both sites as
a basis for characterizing this population
• but since the sample from Site 1 is so large,
lets just use it …
39. • Site 1 suggests that about 20% of our
society belong to this distinct social class…
• if so, we might have expected that 10 of the
50 sites excavated from site 2 would belong
to this class
• but we found only 6…
40. • how likely is it that this difference (10 vs. 6)
could arise just from random chance??
• to answer this question, we have to be
interested in more than just the probability
associated with the single observed
outcome “6”
• we are also interested in the total
probability associated with outcomes that
are more extreme than “6”…
41. • imagine a simulation of the
discovery/excavation process of graves at
Site 2:
• repeated drawing of 50 balls from a jar:
– ca. 800 balls
– 80% black, 20% white
• on average, samples will contain 10 white
balls, but individual samples will vary
42. • by keeping score on how many times we
draw a sample that is as, or more divergent
(relative to the mean sample) than what we
observed in our real-world sample…
• this means we have to tally all samples that
produce 6, 5, 4…0, white balls…
• a tally of just those samples with 6 white
balls eliminates crucial evidence…
43. • we can use the binomial theorem instead of
the drawing experiment, but the same logic
applies
• a cumulative density function (CDF)
displays probabilities associated with a
range of outcomes (such as 6 to 0 graves
with evidence for elite status)
46. • so, the odds are about 1 in 10 that the
differences we see could be attributed to
random effects—rather than social
differences
• you have to decide what this observation
really means, and other kinds of evidence
will probably play a role in your decision…