Consider two gamblers, A and B, who have a combined fortune of n dollars. They bet one dollar each on the toss of a coin.
- If the coin turns up heads, A wins a dollar from B.
- If the coin turns up tails, B wins a dollar from A.
Suppose the successive coin tosses are independent, and the coin turns up heads with probability p and tails with probability q=1-p. The game ends when either A or B is broken (or ruined). Let Xk denote the fortune of gambler A after the k-th toss.
Plot the state transition diagram.
{Xk, k>=0} is a simple random walk on {0,1,2,…, n} with absorbing barriers at 0 and n.
Calculate the stationary distribution of Xk
