Suppose that a person plays a game in which he draws a ball froma box of 10 balls numbered 0 through 9. He then puts the ball backand continue to draw a ball (with replacement) until he drawsanother number which is equal or higher than the first draw. Let Xdenote the number drawn in the first draw and Y denote the numberof subsequent draws needed.
(a) Find the conditional probability distribution of Y given X = x,for x = 0, 1, · · · , 9.
(b) Find the joint probability distribution of X and Y , P(X = x, Y= y).
(c) Find the probability distribution of Y , P(Y = y).
(d) Find E(Y ).
