A biased coin is tossed n times, and heads shows with probability p on each toss. A run is a sequence of throws which result in the same outcome, so that, for example, the sequence HHTHTTH contains five runs. Show that the expected number of runs is 1+2(n-1) p(1- p). Find the variance of the number of runs.
A biased coin is tossed n times, and heads shows with probability p on each toss. A run is a sequence of throws which result in the same outcome, so that, for example, the sequence HHTHTTH contains five runs. Show that the expected number of runs is 1+2(n-1) p(1- p). Find the variance of the number of runs.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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Transcribed Image Text:A biased coin is tossed n times, and heads shows with probability p on each toss. A run is a
sequence of throws which result in the same outcome, so that, for example, the sequence HHTHTTH
contains five runs. Show that the expected number of runs is 1+ 2(n-1) p(1 - p). Find the variance
of the number of runs.
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