Consider a variation of the gambler's ruin problem with parameters p (i.e., the probability that player A wins a game) and N modeled in terms of a random walk with reflecting barrier at zero. Specifically, when state 0 is reached, the process moves to state 1 with probability p0 or stays at state 0 with probability Thus, the only trapping state is N. That is, only player B can be ruined.
a. Give the state transition diagram of the process.
b. If ri is the probability of player B being ruined when the process is currently in state i, obtain the expression for ri to show what happens on the first game when the process is in state i.