Question

Question 3 [10 points] Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 90% of their games. To make up for this, if Doug wins a game he will spot Bob tive points in their next game. if Doug wins again he will spot Bob ten points the next game, and if he still wins the next game he will spot him ifteen points, and continue to spot hinm ifteen points as long as he keeps winning. Whenever Bob wins a game he goes back to playing the next game with no advantage t turns out that with a m oint advantage Bob ns 20% o the time he wins 30% of the time with a ten-point ac van age and 40% f me with a m een polit advantage Model this situation as a Markov chain using the number of consecutive games won by Doug as the states. There should be four states representing zero, ane, two, and three or more consecutive games won by Daug. Find the transition matrix of this system, the steady-state vector for the system, and determine the proportion of games that Doug will win in the long run uncer these conditions P-0 0 0 Proportion of games won by Doug -0

Answer 1

let hansition mabrn A 6ッ 0 q 工ㄚㄚ T)so 30 A-r) DOO 4-1 0028 5 6 627 45 /9 104 141