Question: 22. Let X be a geometric random variable with parameter p, and n and m be nonnegative integers (a) For what values of n is

22. 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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