Question: (1) Let e be a standard exponential random variable. Here, standard means that E[e] = 1. Find E[e e e] by using, for example, the

(1) Let e be a standard exponential random variable. Here, "standard" means that E[e] = 1. Find E[e^ee] by using, for example, the integration by parts to evaluate the underlying Riemann integral. (2) Let X be a standard exponential random variable as in (1). Suppose that the conditional distribution of N given that X = x is Poisson with mean x. Find the probability P(N = 1).

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