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6. An unfair coin is flipped repeatedly, where P(H) = p = 1- q. Let X be the number of flips until HTH first appears, and Y the number of flips until either HTH or THT appears. Show that E(sx) = (p²qs³)/(1-s+ pqs² - pq²s³) and find E(s).

6. An unfair coin is flipped repeatedly, where P(H) = p = 1- q. Let X be the number of flips until HTH first appears, and Y the number of flips until either HTH or THT appears. Show that E(sx) = (p²qs³)/(1-s+ pqs² - pq²s³) and find E(s).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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6. An unfair coin is flipped repeatedly, where P(H) = p = 1- q. Let X be the number of flips until HTH first appears, and Y the number of flips until either HTH or THT appears. Show that E(sx) = (p²qs³)/(1-s+ pqs² - pq²s³) and find E(s).
Transcribed Image Text:6. An unfair coin is flipped repeatedly, where P(H) = p = 1- q. Let X be the number of flips until HTH first appears, and Y the number of flips until either HTH or THT appears. Show that E(sx) = (p²qs³)/(1-s+ pqs² - pq²s³) and find E(s).
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