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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 20: Lecture 22: Transformations and Convolutions | Statistics 110

4.1 ( 11 )

Lecture Details

We discuss transformations of r.v.s (change of variables), the LogNormal distribution, and convolutions (sums). As a bonus, we show how in certain problems one can use probability to prove existence.

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