2. Alice and Bob are playing a game where in each round, each of them rolls a fair die independently. If both roll the same number, then the game is repeated. Otherwise the player with the larger number wins. Let X be the number of rounds until the game is decided. (a) Determine the probability mass function of X. (b) Compute E[X]. (c) Compute Pr[ Alice win]. (d) Assume that you get paid 10USD for winning in the first round, 1USD for winning in any other round, and nothing otherwise. Compute your expected winnings.

2. Alice and Bob are playing a game where in each round, each of them rolls a fair die independently. If both roll the same number, then the game is repeated. Otherwise the player with the larger number wins. Let X be the number of rounds until the game is decided. (a) Determine the probability mass function of X. (b) Compute E[X]. (c) Compute Pr[ Alice win]. (d) Assume that you get paid 10USD for winning in the first round, 1USD for winning in any other round, and nothing otherwise. Compute your expected winnings.

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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