Question: 25. Let X be a geometric random variable with parameter p, and n and m be nonnegative integers. (a) For what values of n is

25. Let X be a geometric random variable with parameter p, and n and m be nonnegative integers.

(a) For what values of n is P(X = n) maximum?

(b) What is the probability that X is even?

(c) Show that the geometric is the only distribution on the positive integers with the memoryless property:

P(X > n +m | X > m) = P(X > n).

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