For each match you play, your probability of winning is 2/3. You plan to play 5 matches, but if you win the fifth match, then you play until you lose. We have the random variables of:  X = "the number of matches you played", Y = “the number of matches you lost” Calculate the expected values EX and EY and the variances Var X and Var Y. Hint: Look at the random variables  X − 5 and Y − 1.

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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For each match you play, your probability of winning is 2/3. You plan to play 5 matches, but if you win the fifth match, then you play until you lose. We have the random variables of: 
X = "the number of matches you played",
Y = “the number of matches you lost”
Calculate the expected values EX and EY and the variances Var X and Var Y. Hint: Look at the random variables  X − 5 and Y − 1.

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