An archer can hit the bull's-eye of the target with probability 1/3. She shoots until she hits the bull's eye or until for shots have been taken. Let the random variable X to be number of shots observed. Assume that the shots are taken independently.

(a) What is the range of X? (That is, what are all the possible values of X?)

(b) Find P (X=4)

(c) After this, the archer starts a new game in which she continues to shoot until she hits the bull's-eye. In this new game, give the mean and standard deviation of random variable Y, the number of shots taken.