Consider independent trials, each of which results in
outcome i,i = 0, 1,... ,k, with probability pi,
Let N denote the number of trials needed to obtain an outcome that is not equal to 0, and let X be that outcome.
(a) Find P{N = n}, n > 1.
(b) Find P{X = j}, j =1,.., k.
(c) Show that P{N = n, X = j} = 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?
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