Suppose you flip a fair coin infinitely many times. Let K₁ be the number of times the pattern HT occurs in the first n flips. 1. What are the expected value and variance of Kn? 2. Prove that Kn/n converges in probability and identify the limit.

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
Section13.3: Special Probability Density Functions
Problem 54E
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Suppose you flip a fair coin infinitely many times. Let K₁ be the number of
times the pattern HT occurs in the first n flips.
1. What are the expected value and variance of Kn?
2. Prove that Kµ/n converges in probability and identify the limit.
Transcribed Image Text:Suppose you flip a fair coin infinitely many times. Let K₁ be the number of times the pattern HT occurs in the first n flips. 1. What are the expected value and variance of Kn? 2. Prove that Kµ/n converges in probability and identify the limit.
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