InfoCoBuild

Statistics 110 - Probability

Statistics 110: Probability (Harvard Univ.). Taught by Professor Joe Blitzstein, this course is an introduction to probability as a language and set of tools for understanding statistics, science, risk, and randomness. The ideas and methods are useful in statistics, science, engineering, economics, finance, and everyday life. Topics include the following. Basics: sample spaces and events, conditioning, Bayes' Theorem. Random variables and their distributions: distributions, moment generating functions, expectation, variance, covariance, correlation, conditional expectation. Univariate distributions: Normal, t, Binomial, Negative Binomial, Poisson, Beta, Gamma. Multivariate distributions: joint, conditional, and marginal distributions, independence, transformations, Multinomial, Multivariate Normal. Limit theorems: law of large numbers, central limit theorem. Markov chains: transition probabilities, stationary distributions, reversibility, convergence.

 Lecture 19 - Joint, Conditional, and Marginal Distributions

This lecture discusses joint, conditional, and marginal distributions, the 2-D LOTUS, the fact that E(XY)=E(X)E(Y) if X and Y are independent, the expected distance between 2 random points, and the chicken-egg problem.

Go to the Course Home or watch other lectures:

 Lecture 01 - Probability and Counting Lecture 02 - Story Proofs, Axioms of Probability Lecture 03 - Birthday Problem, Properties of Probability Lecture 04 - Conditional Probability Lecture 05 - Conditioning Continued, Law of Total Probability Lecture 06 - Monty Hall, Simpson's Paradox Lecture 07 - Gambler's Ruin and Random Variables Lecture 08 - Random Variables and Their Distributions Lecture 09 - Expectation, Indicator Random Variables, Linearity Lecture 10 - Expectation Continued Lecture 11 - The Poisson distribution Lecture 12 - Discrete vs. Continuous, the Uniform Lecture 13 - Normal distribution Lecture 14 - Location, Scale, and LOTUS Lecture 15 - Midterm Review Lecture 16 - Exponential Distribution Lecture 17 - Moment Generating Functions Lecture 18 - MGFs Continued Lecture 19 - Joint, Conditional, and Marginal Distributions Lecture 20 - Multinomial and Cauchy Lecture 21 - Covariance and Correlation Lecture 22 - Transformations and Convolutions Lecture 23 - Beta distribution Lecture 24 - Gamma distribution and Poisson process Lecture 25 - Order Statistics and Conditional Expectation Lecture 26 - Conditional Expectation Continued Lecture 27 - Conditional Expectation given an R.V. Lecture 28 - Inequalities Lecture 29 - Law of Large Numbers and Central Limit Theorem Lecture 30 - Chi-Square, Student-t, Multivariate Normal Lecture 31 - Markov Chains Lecture 32 - Markov Chains Continued Lecture 33 - Markov Chains Continued Further Lecture 34 - A Look Ahead