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Harvard University

Probability

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.

Instructor

Professor Joe Blitzstein,

Mathematics

2013

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