Continue show the problems, both part a and b (see attachment). Please do not use chatgpt, since it not correct

1. (30 pts) Suppose two evenly matched players are equally likely to win when they play against each other (there is no draw). a) (20 pts) They play a series of games until a player has three victories. Let X be the number games played until there is a winner. Find E(X) and SD(X). b) (10 pts) Suppose a player wins after having n victories. Let X be the number of games played, m be the minimum value of X, and M be the maximum value of X. (i) (5 pts) Find m and P(X = m), and plot P(X = m) for n = 1, ..., 10. (ii) (5 pts) Find M and P(X = M), and plot P(X = M) for n = 1, ..., 10. a) 3 4 5 . P ( X = 3) = 2 (4)' = 1 P x ( k) 114 (3/ 8 3/ 8 . P ( X = 4 ) = 2 ( ; ) ( 4 ) " = 2 3 (; ) = . P ( X = 5 ) = I 5.2. 6 - 8