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If we toss a fair coin until we get two consecutive heads or two consecutive tails, let X be the number of tosses. If you toss a fair coin until you get a tail that is preceded by a head, let Y be the number of tosses. (1). Find the PMF of X and E[X]. (2). Find the PMF of Y and E[Y].

If we toss a fair coin until we get two consecutive heads or two consecutive tails, let X be the number of tosses. If you toss a fair coin until you get a tail that is preceded by a head, let Y be the number of tosses. (1). Find the PMF of X and E[X]. (2). Find the PMF of Y and E[Y].

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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If we toss a fair coin until we get two consecutive heads or two consecutive tails, let \(X\) be the number of tosses. If you toss a fair coin until you get a tail that is preceded by a head, let \(Y\) be the number of tosses. (1). Find the PMF of \(X\) and \(\mathbb{E}[X]\). (2). Find the PMF of \(Y\) and \(\mathbb{E}[Y]\).
Transcribed Image Text:If we toss a fair coin until we get two consecutive heads or two consecutive tails, let \(X\) be the number of tosses. If you toss a fair coin until you get a tail that is preceded by a head, let \(Y\) be the number of tosses. (1). Find the PMF of \(X\) and \(\mathbb{E}[X]\). (2). Find the PMF of \(Y\) and \(\mathbb{E}[Y]\).
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