Using Matlab

To win a game of tennis, you need to win at least four points and be ahead by two points. If two players are tied with at least three points, they would say that the score is "deuce." Tennis has several strange terms - most non-tennis players would call it a tie. At that point in the game, there are five states that we could observe as the game continues. These states are Duece (D): When the game is tied, Ad-In (AI): When the server is ahead by one point, Ad-Out (AO): When the receiver is ahead by one point, Service Win (S): When the game has ended with the server winning, and Receiver Win (R): When the game has ended with the reciever winning.

1.) What is the transition matrix for the tennis game in Example 3 with states ordered S, AI, D, AO, R? Assume that the server wins 60% of the points that are played.

2.) Use as many of the random numbers 0.3873, 0.6261, 0.0263, 0.9110, 0.8003, 0.0005, 0.36032, 0.315058, 0.210956, 0.572746 as are needed to simulate the tennis game with the transition matrix you constructed earlier. Assume the game starts at duece (D). Once you reach an absorbing state, you can stop. Repeat the game five times using random pages of a phone book.