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# Statistics 110: Probability

Harvard, , Prof. Joe Blitzstein

Updated On 02 Feb, 19

##### Overview

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 29: Lecture 31: Markov Chains | Statistics 110

4.1 ( 11 )

###### Lecture Details

We introduce Markov chains -- a very beautiful and very useful kind of stochastic process -- and discuss the Markov property, transition matrices, and stationary distributions.

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