(a) From the results of Section 3.6.3 we can conclude that there are n+m-1 m-1 - nonnegative integer valued solutions of the equation xxmn. Prove this directly.

(b) How many positive integer valued solutions of x ++ x = n are there? Hint: Let y, x,- 1.

(c) For the Bose-Einstein distribution, compute the probability that exactly k of the X, are equal to 0.

73. In Section 3.6.3, we saw that if U is a random variable that is uniform on (0, 1) and if, conditional on Up, X is binomial with parameters and p, then P(X = i)= 1 n+1 i = 0, 1,...,n