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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 7: Lecture 9: Expectation, Indicator Random Variables, Linearity | Statistics 110

4.1 ( 11 )

###### Lecture Details

We discuss expected values and the meaning of means, and introduce some very useful tools for finding expected values: indicator r.v.s, linearity, and symmetry. The fundamental bridge connects probability and expectation. We also introduce the Geometric distribution.

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