Balls and bins. There are 10 bins numbered 1, 2, . . . , 10. n balls are thrown into the 10 bins. For each ball, the probability that it falls into bin i is 1 for i = 1, 2, . . . , 10. Different balls

10

are thrown independently of each other. Let Y be the number of balls in bin 1. Let Z be the total number of balls in bins 6, 7, 8, 9, 10.

(a) Find the pmf of Y . (b) Find the pmf of Z.

(c) Find the conditional pmf p(z|y). Please specify the range of y, z. (d) Find the conditional pmf p(y|z). Please specify the range of y, z.