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Suppose you flip a fair coin infinitely many times. Let K₁ be the number of ti e pattern HHHH occurs in the first n flips. What are the expected value and varia f Kn? Is the variance larger or smaller than the variance of a Binomial random vari with the same mean? Can you explain the difference intuitively? For n 100, simu 3000 times and make a histogram of the proportion of times each possible outc = n

Suppose you flip a fair coin infinitely many times. Let K₁ be the number of ti e pattern HHHH occurs in the first n flips. What are the expected value and varia f Kn? Is the variance larger or smaller than the variance of a Binomial random vari with the same mean? Can you explain the difference intuitively? For n 100, simu 3000 times and make a histogram of the proportion of times each possible outc = n

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 6CR
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1. Suppose you flip a fair coin infinitely many times. Let K₁, be the number of times the pattern HHHH occurs in the first n flips. What are the expected value and variance of Kn? Is the variance larger or smaller than the variance of a Binomial random variable with the same mean? Can you explain the difference intuitively? For n = 100, simulate Kn 3000 times and make a histogram of the proportion of times each possible outcome actually occurred in your simulation. Plot this histogram versus the probability mass function of the Binomial random variable with the same mean.
Transcribed Image Text:1. Suppose you flip a fair coin infinitely many times. Let K₁, be the number of times the pattern HHHH occurs in the first n flips. What are the expected value and variance of Kn? Is the variance larger or smaller than the variance of a Binomial random variable with the same mean? Can you explain the difference intuitively? For n = 100, simulate Kn 3000 times and make a histogram of the proportion of times each possible outcome actually occurred in your simulation. Plot this histogram versus the probability mass function of the Binomial random variable with the same mean.
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