(50pts) Joe and Pete each have two cents in their pockets. They have decided to match pennies; they will each take one of their pennies and ip them. If the pennies match (two heads or two tails), Joe gets Pete's penny; if the pennies do not match, Pete gets Joe's penny. They will keep repeating the game until one has four cents, and the other is broke. Although they do not realize it, all four pennies are biased. The probability of tossing a head is 0-3: and the probability of a tail is 0.7. Let X be a. Markov chain where Xn denotes the amount that Joe has after the nth play of the game. (a) Give the onestep Markov matrix for X\". (b) 1What is the probability that Pete will have four pennies after the second toss? (e) 1What is the probability that the game does not end after 10 tosses? ((1) What is expected gains of Joe after 5 tosses