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Introduction to Probability
book

Introduction to Probability

by Joseph K. Blitzstein, Jessica Hwang
September 2015
Beginner content levelBeginner
596 pages
18h 33m
English
CRC Press
Content preview from Introduction to Probability

Chapter 12

Markov chain Monte Carlo

We have seen throughout this book that simulation is a powerful technique in probability. If you can’t convince your friend that it is a good idea to switch doors in the Monty Hall problem, in one second you can simulate playing the game a few thousand times and your friend will just see that switching succeeds about 2/3 of the time. If you’re unsure how to calculate the mean and variance of an r.v. X but you know how to generate i.i.d. draws X1, X2, ... , Xn from that distribution, you can approximate the true mean and true variance using the sample mean and sample variance of the simulated draws:

E(X) 1 n ( X 1 ++ X n ) =  X ¯ n , Var(X) 1 n1 j=1 n ( X j X ¯

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Publisher Resources

ISBN: 9781466575578