In a simplified model of a certain television game show, suppose that the contestant, having won k dollars, will at the next play have k + 1 dollars with probability q and be put out of the game and...

In a simplified model of a certain television game show, suppose that the contestant, having won k dollars, will at the next play have k + 1 dollars with probability q and be put out of the game and leave with nothing with probability p = 1 - q. Suppose that the contestant begins with one dollar. Model her winnings after n plays as a success runs Markov chain by specifying the transition probabilities p_i, q_i, and r_i
in equation (5.15).