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7. (15 pts.) Electrical pulses arrive at random times W1, W2, . .. according to a Poisson process N = (Nt) telo,) of rate A. Suppose the amplitude A(t) for the i-th pulse at time t is given by A;(t) = 0 for t Wi Suppose also the total amplitude at time t is Nt Xt = > Ai(t) i=1 Assume that {Yi}>1 are independent and identically distributed random variables that are independent of {Wi} >1. Suppose Y; has probability density function f on (0, co). Compute the mean total amplitude E[X ]