Question: Let X1, X2, . . . be exponential random variables with parameter 1. (a) Argue that X1 + X2 is not an exponential random variable.

Let X1, X2, . . . be exponential random variables with parameter 1.

(a) Argue that X1 + X2 is not an exponential random variable.

(b) Let N be a geometric random variable with parameter p. Prove that N i=1 Xi is

exponentially distributed with parameter p.

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