Question: 46. If X is a nonnegative integer valued random variable, show that Hint: Define the sequence of random variables In, n 1, by Now

46. If X is a nonnegative integer valued random variable, show that

(a) E[X] = P(X) = P(X > n} m=1 n=0

Hint: Define the sequence of random variables In, n ≥ 1, by

image text in transcribed

Now express X in terms of the In.

(b) If X and Y are both nonnegative integer valued random variables, show that

image text in transcribed

(a) E[X] = P(X) = P(X > n} m=1 n=0

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