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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.

The Soul of Statistics


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

References
Statistics 110: Probability
Instructor: Professor Joe Blitzstein. Handouts. Practice and Solutions. Stat 110 is an introduction to probability as a language and set of tools for understanding statistics, science, risk, and randomness.