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STAT 333 tut9

# STAT 333 tut9 - Stat 333 Tutorial 9 Fall 2011 1 Federer and...

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Stat 333 : Tutorial 9 - Fall 2011 1. Federer and Nadal are playing a series of games for the Wimbledon men’s tennis champi- onship. The ﬁrst player to have a 2 game lead over the other will win the championship. Assume that all games are independent and the probability that Federer wins any one game is 0.675. Let { X n } n 0 be a process such that X n = Federer’s lead over Nadal after n games. (a) Explain why { X n } is a Markov Chain. (b) Provide the one-step transition matrix. (c) Find the probability that Federer wins the championship. (d) Consider now a series of championships between Federer and Nadal. Find the expected number of championships until Federer ﬁrst wins three consecutive championships. (e) As teenagers, Federer and Nadal would practice against each other by playing a series of games. In this case, there were no criteria for a winner. i. Find the probability that Nadal eventually has a 10 game lead over Federer.
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