1. Consider a list of m names, where the same name may appear more than once on the list. Let n(i) denote the number of times that the name in position I appears on the list, i -1,

..., m, and let d denote the number of distinct names on the list.

(a) Express d in terms of the variables m, n, i= 1,..., m.

Let U be a uniform (0, 1) random variable, and let X = [m] + 1.

(b) What is the probability mass function of X?

(c) Argue that E[m/n(X)] = d.