Question

Two gamblers played the following game. A fair coin was tossed. If the outcome is heads, player A pays player B 1$ and if the outcome is tails, player B pays player A 1$. The game is continued until one of the players go broke. Suppose that initially player A has 1$ and player B has 2$. A total of 3$ is up of grabs. Let X(n) denote the number of dollars held by player A after n trials. a) Show that Xn is a markov chain b) Sketch the state transition diagram for Xn and give the one step transition probability matrix p c) Use the state transition diagram to help you show that for n even ...cont.

Answer 1

Cont...(n=2k, Pii(n)=(0.5)^n for i=1,2,... Pi0(n)=2/3[1-0.25^k=P2,3(n)