## Probability

This course is based on: A First Course in Probability (8th Edition) Last Updated: April 29, 2020

Probability gives us the language and framework to think about the future in quantifiable terms so we can plan accordingly (to some degree, since certain things cannot/should not be quantified). It serves as the basis for a lot of other interesting topics such as Statistics, Machine Learning, Game Theory, Risk Analysis, etc.

Recommended Prerequisites: None

Chapter 1
Chapter 1.1: Introduction: What is Combinatorial Analysis
 Combination formula | Probability and combinatorics | Probability and Statistics | Khan Academy Views: 847K; Net Likes: 3.88K; Like Ratio: 96%; Length: 11m Permutation formula | Probability and combinatorics | Probability and Statistics | Khan Academy Views: 878K; Net Likes: 3.72K; Like Ratio: 97%; Length: 7m Factorials Explained! Views: 204K; Net Likes: 3.69K; Like Ratio: 98%; Length: 11m 6 Introduction to Backtracking - Brute Force Approach Views: 310K; Net Likes: 3.44K; Like Ratio: 98%; Length: 8m
Chapter 1.2: Basic Principle of Counting
 Counting Principle, Permutations, and Combinations Views: 92.4K; Net Likes: 925; Like Ratio: 97%; Length: 24m Multiplication Principle - Counting Techniques Views: 191K; Net Likes: 891; Like Ratio: 97%; Length: 10m Permutations and Combinations 1 (Counting principle) Views: 35.6K; Net Likes: 562; Like Ratio: 97%; Length: 10m The Fundamental Counting Principle - Lesson Views: 21.1K; Net Likes: 214; Like Ratio: 97%; Length: 37m
Chapter 1.3: Permutations & Combinations
 Permutations and Combinations Tutorial Views: 426K; Net Likes: 6.51K; Like Ratio: 98%; Length: 17m Permutation and Combination - Shortcuts & Tricks for Placement Tests, Job Interviews & Exams Views: 484K; Net Likes: 5.46K; Like Ratio: 95%; Length: 1H11m Permutation formula | Probability and combinatorics | Probability and Statistics | Khan Academy Views: 878K; Net Likes: 3.72K; Like Ratio: 97%; Length: 7m Permutations Views: 935K; Net Likes: 2.91K; Like Ratio: 96%; Length: 10m
Chapter 1.4: Multinomial Coefficients
 Multinomial theorem Part I | Permutation and combination | JEE Maths by Ghanshyam Tewani | Cengage Views: 28K; Net Likes: 731; Like Ratio: 98%; Length: 34m Multinomial Logistic Regression with R: Categorical Response Variable at Three Levels Views: 65.4K; Net Likes: 533; Like Ratio: 99%; Length: 15m Generalizing with binomial coefficients (bit advanced) | Probability and Statistics | Khan Academy Views: 264K; Net Likes: 506; Like Ratio: 96%; Length: 11m Interpreting Odds Ratio for Multinomial Logistic Regression using SPSS - Nominal and Scale Variables Views: 48.9K; Net Likes: 486; Like Ratio: 98%; Length: 13m
Chapter 2
Chapter 2.1: Introduction: What is Probability
 Intro to Conditional Probability Views: 413K; Net Likes: 4.3K; Like Ratio: 96%; Length: 6m #1 | Probability (Part-1) | basic introduction | CA | CS | CMA | Bcom | BBA | Eco h | Views: 231K; Net Likes: 2.73K; Like Ratio: 97%; Length: 4m Introduction to Probability, Basic Overview - Sample Space, & Tree Diagrams Views: 177K; Net Likes: 2.7K; Like Ratio: 98%; Length: 16m Statistics Lecture 4.2: Introduction to Probability Views: 327K; Net Likes: 2.51K; Like Ratio: 97%; Length: 1H42m
Chapter 2.2: Sample Space and Events
 Probability of Complementary Events & Sample Space Views: 35.7K; Net Likes: 496; Like Ratio: 99%; Length: 5m Probability: Lesson 2 - Sample Space, Events and Compound Events Views: 99.3K; Net Likes: 492; Like Ratio: 98%; Length: 21m Probability - Sample Space, Sample Points, Events! Views: 60.8K; Net Likes: 475; Like Ratio: 96%; Length: 1m SAMPLE SPACE (DEFINITION) ( PROBABILITY ) Views: 10.5K; Net Likes: 197; Like Ratio: 96%; Length: 2m
Chapter 2.3: Axioms of Probability
 1. Probability Models and Axioms Views: 808K; Net Likes: 3.97K; Like Ratio: 98%; Length: 51m Multiplication & Addition Rule - Probability - Mutually Exclusive & Independent Events Views: 216K; Net Likes: 2.5K; Like Ratio: 97%; Length: 10m Probability of Complementary Events & Sample Space Views: 35.7K; Net Likes: 496; Like Ratio: 99%; Length: 5m Probability & Random Variables - Week 2 - Lecture 1 - Probability Spaces; Axioms and properties .. Views: 153K; Net Likes: 478; Like Ratio: 95%; Length: 46m
Chapter 2.4: Probability as a Measure of Belief
 2017 Maps of Meaning 08: Neuropsychology of Symbolic Representation Views: 547K; Net Likes: 7.45K; Like Ratio: 96%; Length: 2H21m 2017 Maps of Meaning 12: Final: The Divinity of the Individual Views: 409K; Net Likes: 7.05K; Like Ratio: 97%; Length: 2H25m PHILOSOPHY - Epistemology: Introduction to Theory of Knowledge [HD] Views: 442K; Net Likes: 4.12K; Like Ratio: 97%; Length: 6m Making Probability Mathematical | Infinite Series Views: 114K; Net Likes: 2.76K; Like Ratio: 98%; Length: 14m
Chapter 3
Chapter 3.1: Introduction: What is Conditional Probability
 Conditional Probability Views: 214K; Net Likes: 2.64K; Like Ratio: 97%; Length: 12m Basic probability: Joint, marginal and conditional probability | Independence Views: 111K; Net Likes: 2.18K; Like Ratio: 99%; Length: 14m Conditional probability explained visually (Bayes' Theorem) Views: 440K; Net Likes: 1.5K; Like Ratio: 96%; Length: 5m An Introduction to Conditional Probability Views: 101K; Net Likes: 1.37K; Like Ratio: 99%; Length: 12m
Chapter 3.2: Bayes's Formula
 Bayes theorem Views: 716K; Net Likes: 34.4K; Like Ratio: 99%; Length: 15m The quick proof of Bayes' theorem Views: 267K; Net Likes: 9.23K; Like Ratio: 99%; Length: 3m Bayes' Theorem - The Simplest Case Views: 522K; Net Likes: 4.76K; Like Ratio: 95%; Length: 5m CRITICAL THINKING - Fundamentals: Bayes' Theorem [HD] Views: 310K; Net Likes: 4.58K; Like Ratio: 97%; Length: 6m
Chapter 3.3: Independent Events
 Multiplication & Addition Rule - Probability - Mutually Exclusive & Independent Events Views: 216K; Net Likes: 2.5K; Like Ratio: 97%; Length: 10m Compound probability of independent events | Probability and Statistics | Khan Academy Views: 913K; Net Likes: 1.46K; Like Ratio: 96%; Length: 6m Independent Events (Basics of Probability: Independence of Two Events) Views: 79.5K; Net Likes: 859; Like Ratio: 98%; Length: 21m Probability - Independent and Dependent Events Views: 57.5K; Net Likes: 756; Like Ratio: 98%; Length: 10m
Chapter 4
Chapter 4.1: Random Variables
 Expected Value and Variance of Discrete Random Variables Views: 542K; Net Likes: 4.2K; Like Ratio: 96%; Length: 7m Discrete and continuous random variables | Probability and Statistics | Khan Academy Views: 1.22M; Net Likes: 3.92K; Like Ratio: 95%; Length: 11m Introduction to Random Variables Views: 872K; Net Likes: 2.77K; Like Ratio: 96%; Length: 12m Continuous Random Variables: Probability Density Functions Views: 216K; Net Likes: 1.99K; Like Ratio: 98%; Length: 23m
Chapter 4.2: Discrete Random Variables
 Expected Value and Variance of Discrete Random Variables Views: 542K; Net Likes: 4.2K; Like Ratio: 96%; Length: 7m Discrete and continuous random variables | Probability and Statistics | Khan Academy Views: 1.22M; Net Likes: 3.92K; Like Ratio: 95%; Length: 11m Discrete vs. Continuous Relationships Tutorial Views: 146K; Net Likes: 2.43K; Like Ratio: 97%; Length: 5m Introduction to Discrete Random Variables and Discrete Probability Distributions Views: 285K; Net Likes: 1.86K; Like Ratio: 97%; Length: 11m
Chapter 4.3: Expectation and Variance of a Random Variable
 The Basics Of Poker EV | Poker Quick Plays Views: 260K; Net Likes: 3.31K; Like Ratio: 97%; Length: 7m Decision Analysis 2: EMV & EVPI - Expected Value & Perfect Information Views: 339K; Net Likes: 2.11K; Like Ratio: 97%; Length: 3m Expected Value Views: 315K; Net Likes: 1.67K; Like Ratio: 96%; Length: 7m Statistics 101: Expected Value Views: 105K; Net Likes: 1.59K; Like Ratio: 99%; Length: 21m
Chapter 4.4: Bernoulli Random Variable
 Introduction to the Bernoulli Distribution Views: 217K; Net Likes: 1.78K; Like Ratio: 98%; Length: 5m Finding The Probability of a Binomial Distribution Plus Mean & Standard Deviation Views: 140K; Net Likes: 1.7K; Like Ratio: 97%; Length: 20m Bernoulli, Binomial and Poisson Random Variables Views: 127K; Net Likes: 1.11K; Like Ratio: 97%; Length: 25m 13. Bernoulli Process Views: 65.7K; Net Likes: 409; Like Ratio: 97%; Length: 50m
Chapter 4.5: Binomial Random Variable
 The Binomial Distribution: Crash Course Statistics #15 Views: 165K; Net Likes: 2.78K; Like Ratio: 97%; Length: 14m The Binomial Distribution / Binomial Probability Function Views: 473K; Net Likes: 2.38K; Like Ratio: 97%; Length: 6m Finding Binomial Probabilities Using the TI-84 Views: 382K; Net Likes: 1.9K; Like Ratio: 96%; Length: 15m Finding The Probability of a Binomial Distribution Plus Mean & Standard Deviation Views: 140K; Net Likes: 1.7K; Like Ratio: 97%; Length: 20m
Chapter 4.6: Geometric Random Variable
 Geometric Distributions and The Birthday Paradox: Crash Course Statistics #16 Views: 83.1K; Net Likes: 1.72K; Like Ratio: 98%; Length: 10m Geometric Distribution - Probability, Mean, Variance, & Standard Deviation Views: 31.6K; Net Likes: 368; Like Ratio: 97%; Length: 32m AP Statistics: Binomial and Geometric Random Variables Views: 6.63K; Net Likes: 250; Like Ratio: 100%; Length: 46m Geometric random variables introduction | Random variables | AP Statistics | Khan Academy Views: 35.8K; Net Likes: 185; Like Ratio: 97%; Length: 6m
Chapter 4.7: Hypergeometric Random Variable
 An Introduction to the Hypergeometric Distribution Views: 173K; Net Likes: 1.57K; Like Ratio: 99%; Length: 15m The Hypergeometric Distribution: An Introduction (fast version) Views: 160K; Net Likes: 1.44K; Like Ratio: 97%; Length: 9m Geometric Distribution - Probability, Mean, Variance, & Standard Deviation Views: 31.6K; Net Likes: 368; Like Ratio: 97%; Length: 32m 18. Hypergeometric Distribution - Probability - Gate Views: 16.3K; Net Likes: 290; Like Ratio: 98%; Length: 8m
Chapter 4.8: Expected Value of Sums of Random Variables
 The Expected Value and Variance of Discrete Random Variables Views: 175K; Net Likes: 1.51K; Like Ratio: 98%; Length: 11m Find Mean or Expectation of Sum of Numbers for Two Dice Views: 12.6K; Net Likes: 128; Like Ratio: 96%; Length: 8m L12.2 The Sum of Independent Discrete Random Variables Views: 10.7K; Net Likes: 90; Like Ratio: 97%; Length: 7m Example of expected value and variance of a sum of two independent random variables Views: 12K; Net Likes: 40; Like Ratio: 100%; Length: 15m
Chapter 4.9: Poisson Random Variable
 The Poisson Distribution Views: 736K; Net Likes: 3.61K; Like Ratio: 96%; Length: 5m Poisson or Not? (When does a random variable have a Poisson distribution?) Views: 153K; Net Likes: 1.66K; Like Ratio: 98%; Length: 14m Bernoulli, Binomial and Poisson Random Variables Views: 127K; Net Likes: 1.11K; Like Ratio: 97%; Length: 25m The Poisson Distribution: Mathematically Deriving the Mean and Variance Views: 88.9K; Net Likes: 881; Like Ratio: 99%; Length: 9m
Chapter 4.10: Cumulative Distribution Function
 Continuous Random Variables: Cumulative Distribution Functions Views: 140K; Net Likes: 1.44K; Like Ratio: 98%; Length: 25m Random Variable, Probability Density Function, Cumulative Distribution Function Views: 102K; Net Likes: 1.35K; Like Ratio: 95%; Length: 21m Cumulative Distribution Functions : Introduction | ExamSolutions Views: 150K; Net Likes: 529; Like Ratio: 98%; Length: 12m Cumulative Distribution Function : Example | ExamSolutions Views: 182K; Net Likes: 525; Like Ratio: 95%; Length: 9m
Chapter 5
Chapter 5.1: Continuous Random Variables
 An Introduction to Continuous Probability Distributions Views: 367K; Net Likes: 2.03K; Like Ratio: 98%; Length: 5m Continuous Random Variables: Probability Density Functions Views: 217K; Net Likes: 2K; Like Ratio: 98%; Length: 23m Continuous Random Variables: Cumulative Distribution Functions Views: 140K; Net Likes: 1.44K; Like Ratio: 98%; Length: 25m Random Variable, Probability Density Function, Cumulative Distribution Function Views: 102K; Net Likes: 1.35K; Like Ratio: 95%; Length: 21m
Chapter 5.2: Expectation and Variance of a Continuous Random Variable
 Continuous Random Variables: Mean & Variance Views: 151K; Net Likes: 1.23K; Like Ratio: 98%; Length: 14m Deriving the Mean and Variance of a Continuous Probability Distribution Views: 130K; Net Likes: 1.09K; Like Ratio: 98%; Length: 7m Mean E(X) and Variance Var(X) for Continuous Random Variables Views: 99K; Net Likes: 342; Like Ratio: 96%; Length: 8m 29-Functions of Continuous Random Variables Views: 22.6K; Net Likes: 163; Like Ratio: 96%; Length: 11m
Chapter 5.3: Uniform Random Variable
 Continuous probability distribution intro Views: 209K; Net Likes: 936; Like Ratio: 97%; Length: 9m Uniform Distribution | Rectangular Distribution | Mean & Variance | Moment Generating Function Views: 26K; Net Likes: 500; Like Ratio: 98%; Length: 10m Continuous Probability Uniform Distribution Problems Views: 25.2K; Net Likes: 332; Like Ratio: 99%; Length: 31m Uniform Distribution Views: 36.2K; Net Likes: 229; Like Ratio: 95%; Length: 15m
Chapter 5.4: Normal Random Variable
 An Introduction to the Normal Distribution Views: 483K; Net Likes: 2.74K; Like Ratio: 97%; Length: 5m 03 - The Normal Probability Distribution Views: 218K; Net Likes: 2.28K; Like Ratio: 97%; Length: 20m Normal Distribution & Probability Problems Views: 165K; Net Likes: 1.61K; Like Ratio: 96%; Length: 29m Standardizing Normally Distributed Random Variables Views: 202K; Net Likes: 1.45K; Like Ratio: 98%; Length: 10m
Chapter 5.5: Exponential Random Variable
 Exponential Distribution | Mean & Variance | Moment Generating Function Views: 35K; Net Likes: 711; Like Ratio: 97%; Length: 9m Exponential Distribution Views: 82.8K; Net Likes: 463; Like Ratio: 97%; Length: 22m Probability Exponential Distribution Problems Views: 33.1K; Net Likes: 355; Like Ratio: 98%; Length: 10m Exponential Distribution! Definition | Calculations | Why is it called "Exponential"? Views: 9.73K; Net Likes: 271; Like Ratio: 99%; Length: 22m
Chapter 5.6: Gamma Distribution
 The Gamma Function, its Properties, and Application to Bessel Functions Views: 48.8K; Net Likes: 575; Like Ratio: 97%; Length: 14m Lecture 24: Gamma distribution and Poisson process | Statistics 110 Views: 87.5K; Net Likes: 485; Like Ratio: 97%; Length: 48m Gamma Distribution Lesson from Actuarial Path Views: 11.8K; Net Likes: 107; Like Ratio: 97%; Length: 27m Exam P MUST KNOW | Gamma Distribution Views: 4.43K; Net Likes: 67; Like Ratio: 100%; Length: 34m
Chapter 5.7: Weibull Distribution
 Introduction to Weibull Analysis Views: 3.47K; Net Likes: 204; Like Ratio: 99%; Length: 26m Tutorial for determining Weibull modulus in excel Views: 34.5K; Net Likes: 185; Like Ratio: 95%; Length: 6m 10/26/2016 Intro to MSE weibull statistics and probabilistic design Views: 13.7K; Net Likes: 161; Like Ratio: 99%; Length: 31m Weibull distribution -- Example 1 Views: 40.9K; Net Likes: 132; Like Ratio: 96%; Length: 5m
Chapter 5.8: Beta Distribution
 PMP Exam Preparation: Introduction to Three Point Estimating Views: 93.9K; Net Likes: 503; Like Ratio: 97%; Length: 9m 19 - Beta distribution - an introduction Views: 76.6K; Net Likes: 466; Like Ratio: 96%; Length: 10m Lecture 23: Beta distribution | Statistics 110 Views: 56.3K; Net Likes: 366; Like Ratio: 98%; Length: 49m Continuous Distributions: Beta and Dirichlet Distributions Views: 16.7K; Net Likes: 272; Like Ratio: 97%; Length: 18m
Chapter 5.9: Distribution of a Function of a Random Variable
 Discrete and continuous random variables | Probability and Statistics | Khan Academy Views: 1.22M; Net Likes: 3.92K; Like Ratio: 95%; Length: 11m Continuous Random Variables: Probability Density Functions Views: 217K; Net Likes: 2K; Like Ratio: 98%; Length: 23m Constructing a probability distribution for random variable | Khan Academy Views: 831K; Net Likes: 1.7K; Like Ratio: 96%; Length: 6m Random Variable, Probability Mass Function, Distribution Function Views: 116K; Net Likes: 1.65K; Like Ratio: 97%; Length: 18m
Chapter 6
Chapter 6.1: Joint Distribution Functions
 Joint Probability Distribution (continuous random variables) Views: 109K; Net Likes: 1.25K; Like Ratio: 96%; Length: 19m Lecture 19: Joint, Conditional, and Marginal Distributions | Statistics 110 Views: 164K; Net Likes: 844; Like Ratio: 96%; Length: 50m Joint Probability Distribution , Joint PMF, Marginal PMF, Bivariate RV Views: 50.9K; Net Likes: 762; Like Ratio: 96%; Length: 20m Joint probability distribution for discrete random variable GOOD example(PART-1) Views: 43.3K; Net Likes: 536; Like Ratio: 96%; Length: 11m
Chapter 6.2: Independent Random Variables
 The Sum of Discrete and Continuous Random Variables Views: 30.7K; Net Likes: 156; Like Ratio: 97%; Length: 5m L12.2 The Sum of Independent Discrete Random Variables Views: 10.8K; Net Likes: 92; Like Ratio: 96%; Length: 7m MA 381: Section 8.2: Independent Random Variables Views: 7.38K; Net Likes: 41; Like Ratio: 96%; Length: 9m L07.4 Independence of Random Variables Views: 5.73K; Net Likes: 34; Like Ratio: 100%; Length: 5m
Chapter 6.3: Sums of Independent Random Variables
 L12.2 The Sum of Independent Discrete Random Variables Views: 10.8K; Net Likes: 92; Like Ratio: 96%; Length: 7m Linear Combinations 2.1 Introduction, sums, multiples, mean and variance Views: 9.87K; Net Likes: 92; Like Ratio: 99%; Length: 9m L12.7 The Variance of the Sum of Random Variables Views: 5.17K; Net Likes: 37; Like Ratio: 95%; Length: 5m L07.4 Independence of Random Variables Views: 5.73K; Net Likes: 34; Like Ratio: 100%; Length: 5m
Chapter 6.4: Order Statistics
 Lecture 25: Order Statistics and Conditional Expectation | Statistics 110 Views: 53.2K; Net Likes: 254; Like Ratio: 96%; Length: 48m Order Statistics 1 Views: 23.1K; Net Likes: 189; Like Ratio: 97%; Length: 11m Lec 6 | MIT 6.046J / 18.410J Introduction to Algorithms (SMA 5503), Fall 2005 Views: 76.1K; Net Likes: 182; Like Ratio: 98%; Length: 1H8m Order statistics -- Example 1 Views: 19.4K; Net Likes: 86; Like Ratio: 97%; Length: 12m
Chapter 6.5: Joint Probability Distribution of Functions of Random Variables
 Constructing a probability distribution for random variable | Khan Academy Views: 831K; Net Likes: 1.7K; Like Ratio: 96%; Length: 6m Joint Probability Distribution (continuous random variables) Views: 109K; Net Likes: 1.25K; Like Ratio: 96%; Length: 19m Lecture 19: Joint, Conditional, and Marginal Distributions | Statistics 110 Views: 164K; Net Likes: 844; Like Ratio: 96%; Length: 50m Joint Probability Distribution , Joint PMF, Marginal PMF, Bivariate RV Views: 50.9K; Net Likes: 762; Like Ratio: 96%; Length: 20m
Chapter 7
Chapter 7.1: Expectation and Variance of Sums of Random Variables
 Lecture 9: Expectation, Indicator Random Variables, Linearity | Statistics 110 Views: 88.9K; Net Likes: 429; Like Ratio: 97%; Length: 50m Find Mean or Expectation of Sum of Numbers for Two Dice Views: 12.6K; Net Likes: 128; Like Ratio: 96%; Length: 8m L12.2 The Sum of Independent Discrete Random Variables Views: 10.8K; Net Likes: 92; Like Ratio: 96%; Length: 7m Ch9Pr45: Expectation of Continuous Random Variables Views: 7.4K; Net Likes: 45; Like Ratio: 100%; Length: 12m
Chapter 7.2: Covariance
 Random Processes - 04 - Mean and Autocorrelation Function Example Views: 106K; Net Likes: 780; Like Ratio: 97%; Length: 8m Lecture 21: Covariance and Correlation | Statistics 110 Views: 77.2K; Net Likes: 458; Like Ratio: 96%; Length: 49m Linear Combinations 2.1 Introduction, sums, multiples, mean and variance Views: 9.87K; Net Likes: 92; Like Ratio: 99%; Length: 9m (PP 6.10) Sum of independent Gaussians Views: 9.16K; Net Likes: 47; Like Ratio: 98%; Length: 13m
Chapter 7.3: Correlations
 The Correlation Coefficient - Explained in Three Steps Views: 588K; Net Likes: 6.14K; Like Ratio: 98%; Length: 6m #1 | Correlation | Meaning Views: 289K; Net Likes: 3.33K; Like Ratio: 97%; Length: 4m Covariance and Correlation Part 1: Covariance Views: 102K; Net Likes: 2.51K; Like Ratio: 98%; Length: 22m The danger of mixing up causality and correlation: Ionica Smeets at TEDxDelft Views: 324K; Net Likes: 1.78K; Like Ratio: 98%; Length: 5m
Chapter 7.4: Moment Generating Functions
 Binomial Distribution | Mean & Variance | Moment Generating Function Views: 101K; Net Likes: 1.75K; Like Ratio: 96%; Length: 16m What are "moments" in statistics? An intuitive video! Views: 22.1K; Net Likes: 728; Like Ratio: 99%; Length: 15m Lecture 17: Moment Generating Functions | Statistics 110 Views: 98.8K; Net Likes: 395; Like Ratio: 98%; Length: 50m Moment Generating Functions (Part 1) Views: 21.8K; Net Likes: 339; Like Ratio: 96%; Length: 8m
Chapter 7.5: General Definition of Expectation
 Conditional Probability given Joint PDF Views: 49.7K; Net Likes: 526; Like Ratio: 98%; Length: 12m Lecture 25: Order Statistics and Conditional Expectation | Statistics 110 Views: 53.2K; Net Likes: 254; Like Ratio: 96%; Length: 48m Conditional expectation -- Example 1 Views: 43.9K; Net Likes: 237; Like Ratio: 98%; Length: 3m Lecture 27: Conditional Expectation given an R.V. | Statistics 110 Views: 43.8K; Net Likes: 210; Like Ratio: 97%; Length: 50m
Chapter 8
Chapter 8.1: Chebyshev's Inequality
 Problem Using Chebyshev's Theorem Views: 260K; Net Likes: 1.65K; Like Ratio: 98%; Length: 5m L18.3 The Chebyshev Inequality Views: 30.3K; Net Likes: 249; Like Ratio: 97%; Length: 5m STATISTICS- Chebyshev's InEquality Views: 14K; Net Likes: 217; Like Ratio: 95%; Length: 4m S18.2 Jensen's Inequality Views: 12K; Net Likes: 192; Like Ratio: 99%; Length: 12m
Chapter 8.2: Weak Law of Large Numbers
 Law of Large Numbers - Explained and Visualized Views: 100K; Net Likes: 1K; Like Ratio: 97%; Length: 4m Lecture 29: Law of Large Numbers and Central Limit Theorem | Statistics 110 Views: 89.7K; Net Likes: 672; Like Ratio: 97%; Length: 49m 19. Weak Law of Large Numbers Views: 48.9K; Net Likes: 296; Like Ratio: 98%; Length: 50m A proof of the weak law of large numbers Views: 38.6K; Net Likes: 243; Like Ratio: 97%; Length: 4m
Chapter 8.3: Central Limit Theorem
 Introduction to the Central Limit Theorem Views: 384K; Net Likes: 3.14K; Like Ratio: 98%; Length: 13m The Central Limit Theorem Views: 94.8K; Net Likes: 2.49K; Like Ratio: 98%; Length: 7m What is the CENTRAL LIMIT THEOREM? and why is it so hard to understand?? Views: 182K; Net Likes: 1.85K; Like Ratio: 97%; Length: 8m 02 - What is the Central Limit Theorem in Statistics? - Part 1 Views: 117K; Net Likes: 1.7K; Like Ratio: 98%; Length: 32m
Chapter 8.4: Strong Law of Large Numbers
 Law of Large Numbers - Explained and Visualized Views: 99.8K; Net Likes: 993; Like Ratio: 97%; Length: 4m Lecture 29: Law of Large Numbers and Central Limit Theorem | Statistics 110 Views: 89.6K; Net Likes: 672; Like Ratio: 97%; Length: 49m 19. Weak Law of Large Numbers Views: 48.8K; Net Likes: 296; Like Ratio: 98%; Length: 50m A proof of the weak law of large numbers Views: 38.5K; Net Likes: 241; Like Ratio: 97%; Length: 4m
Chapter 8.5: Chernoff Bounds
 Probabilty Bounds Views: 16.1K; Net Likes: 123; Like Ratio: 97%; Length: 10m S18.3 Hoeffding's Inequality Views: 8.09K; Net Likes: 95; Like Ratio: 100%; Length: 18m Al "Alley Cat" Chernoff, Oct 18, 2014 Views: 2.04K; Net Likes: 58; Like Ratio: 100%; Length: 57Sm Concentration Bounds Views: 6.08K; Net Likes: 30; Like Ratio: 97%; Length: 24m
Chapter 8.6: Jensen's Inequality
 S18.2 Jensen's Inequality Views: 12K; Net Likes: 191; Like Ratio: 99%; Length: 12m 015 Jensen's inequality & Kullback Leibler divergence Views: 4.36K; Net Likes: 80; Like Ratio: 97%; Length: 9m Information Inequalities Views: 3.29K; Net Likes: 18; Like Ratio: 100%; Length: 55m Jensen's Inequality Example 1 Views: 332; Net Likes: 6; Like Ratio: 100%; Length: 13m
Chapter 9
Chapter 9.1: Poisson Process
 Poisson process 2 | Probability and Statistics | Khan Academy Views: 406K; Net Likes: 1.04K; Like Ratio: 95%; Length: 12m 14. Poisson Process I Views: 95.4K; Net Likes: 493; Like Ratio: 97%; Length: 52m Lecture 24: Gamma distribution and Poisson process | Statistics 110 Views: 87.5K; Net Likes: 486; Like Ratio: 97%; Length: 48m 15. Poisson Process II Views: 45.2K; Net Likes: 301; Like Ratio: 99%; Length: 49m
Chapter 9.2: Markov Chains
 A friendly introduction to Bayes Theorem and Hidden Markov Models Views: 245K; Net Likes: 6.74K; Like Ratio: 99%; Length: 32m Can a Chess Piece Explain Markov Chains? | Infinite Series Views: 153K; Net Likes: 4.55K; Like Ratio: 99%; Length: 13m Markov Chains - Part 1 Views: 670K; Net Likes: 3.23K; Like Ratio: 96%; Length: 12m Finite Math: Markov Chain Example - The Gambler's Ruin Views: 142K; Net Likes: 2.17K; Like Ratio: 98%; Length: 20m
Chapter 9.3: Coding Theory and Entropy
 A Short Introduction to Entropy, Cross-Entropy and KL-Divergence Views: 140K; Net Likes: 5.83K; Like Ratio: 99%; Length: 10m Shannon Entropy and Information Gain Views: 93.6K; Net Likes: 2.82K; Like Ratio: 98%; Length: 21m Lecture 1: Introduction to Information Theory Views: 182K; Net Likes: 1.41K; Like Ratio: 97%; Length: 1H1m Information entropy | Journey into information theory | Computer Science | Khan Academy Views: 161K; Net Likes: 1.41K; Like Ratio: 98%; Length: 7m
Chapter 10
Chapter 10.1: General Techniques for Simulating Continuous Random Variables
 An introduction to inverse transform sampling Views: 20.1K; Net Likes: 275; Like Ratio: 98%; Length: 11m Simulation showing bias in sample variance | Probability and Statistics | Khan Academy Views: 113K; Net Likes: 258; Like Ratio: 98%; Length: 6m Probability functions: pdf, CDF and inverse CDF (FRM T2-1) Views: 25.6K; Net Likes: 242; Like Ratio: 99%; Length: 20m Mean, Variance, and Standard Deviation of Discrete Random Variable-TI-84 Views: 24.2K; Net Likes: 196; Like Ratio: 97%; Length: 8m
Chapter 10.2: Simulating from Discrete Distributions
 Discrete and continuous random variables | Probability and Statistics | Khan Academy Views: 1.22M; Net Likes: 3.92K; Like Ratio: 95%; Length: 11m Discrete vs. Continuous Relationships Tutorial Views: 146K; Net Likes: 2.43K; Like Ratio: 97%; Length: 5m Introduction to the Bernoulli Distribution Views: 218K; Net Likes: 1.78K; Like Ratio: 98%; Length: 5m Constructing a probability distribution for random variable | Khan Academy Views: 831K; Net Likes: 1.7K; Like Ratio: 96%; Length: 6m
Chapter 10.3: Variance Reduction Techniques
 MC simulations: 3.2 Control variate Views: 3.88K; Net Likes: 45; Like Ratio: 98%; Length: 16m Stochastic Variance Reduction Methods for Policy Evaluation Views: 787; Net Likes: 6; Like Ratio: 100%; Length: 47m Variance reduction Views: 780; Net Likes: 3; Like Ratio: 100%; Length: 7m Frederic Legoll: Variance reduction approaches for stochastic homogenization Views: 373; Net Likes: 3; Like Ratio: 100%; Length: 44m