24. Consider independent trials each of which results in outcome i, i = 0, 1,..., k with probability p Σ 1. Let N denote the number of trials 1-0 needed to obtain an outcome that is not equal to 0, and let X be that outcome.

(a) Find P(N), л≥ 1.

(b) Find P(X= j).1......

(c) Show that PIN = n, Xj] = P(N = n) P(X = j).

(d) Is it intuitive to you that N is independent of X?

(e) Is it intuitive to you that X is independent of N?