It is apparent from the definition of variance that if X is a constant, then V[X] =

Question:

It is apparent from the definition of variance that if X is a constant, then V[X] = 0. Here we show the converse.
(a) Suppose X is a nonnegative discrete random variable with E[X] = 0. Show that P(X = 0) = 1.
(b) Let X be a discrete random variable with E[X] = μ and V[X] = 0. Show that P(X = μ) = 1.

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