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Two teams A and B are playing in a three-game series. The series ends as soon as one of the teams wins two games. Let X denote the outcome between the two teams; possible values for X are AA (team A wins in two straight games), BAA (team B wins first game, then loses two straight), etc. Let Y e {2,3} denote the number of games played. Assume that the two teams are evenly matched (i.c. cach team is equally likely to win a given game) and outcomes of games are independent.

Two teams A and B are playing in a three-game series. The series ends as soon as one of the teams wins two games. Let X denote the outcome between the two teams; possible values for X are AA (team A wins in two straight games), BAA (team B wins first game, then loses two straight), etc. Let Y e {2,3} denote the number of games played. Assume that the two teams are evenly matched (i.c. cach team is equally likely to win a given game) and outcomes of games are independent.

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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1. Two teams A and B are playing in a three-game series. The series ends as soon as one of the teams wins two games. Let X denote the outcome between the two teams; possible values for X are AA (team A wins in two straight games), BAA (tcam B wins first game, then loses two straight), ctc. Let Y E {2, 3} denote the number of games played. Assume that the two teams are evenly matched (i.e. cach team is equally likely to win a given game) and outcomes of games are independent. (a) Calculate H(X). (b) Calculate H(Y). (c) Calculate H(X|Y).
Transcribed Image Text:1. Two teams A and B are playing in a three-game series. The series ends as soon as one of the teams wins two games. Let X denote the outcome between the two teams; possible values for X are AA (team A wins in two straight games), BAA (tcam B wins first game, then loses two straight), ctc. Let Y E {2, 3} denote the number of games played. Assume that the two teams are evenly matched (i.e. cach team is equally likely to win a given game) and outcomes of games are independent. (a) Calculate H(X). (b) Calculate H(Y). (c) Calculate H(X|Y).
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