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Suppose that X follows geometric distribution with the probability of success p, where 0 < p...

Suppose that X follows geometric distribution with the probability of success p, where 0 < p < 1, and probability of failure 1 − p = q. The pmf is given by f(x) = P(X = x) = q x−1p, x = 1, 2, 3, 4, . . . . Show that X is a pmf. Compute the mean and variance of X without using moment generating function technique. Show all steps.

To compute the variance of X, first compute E[X2]. To find that use the logic that we used in class two times consecutively.

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