x # 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 18: Lecture 20: Multinomial and Cauchy | Statistics 110

4.1 ( 11 )

###### Lecture Details

We introduce the Multinomial distribution, which is arguably the most important multivariate discrete distribution, and discuss its story and some of its nice properties, such as being able to "lump" categories together. We also do an example with the Cauchy distribution.

Note: Around 7:39, a factor of the square root of 2 was accidentally
dropped; the result should be 2 over the square root of pi, rather
than the square root of 2 over pi.

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Excellent course helped me understand topic that i couldn't while attendinfg my college. 