6.2. Shocks occur to a system according to a Poisson process of intensity A. Each shock causes some damage to the system, and these damages accumulate. Let N(t) be the number of shocks up to time t, and let Y be the damage caused by the ith shock. Then

is the total damage up to time t. Determine the mean and variance of the total damage at time t when the individual shock damages are exponentially distributed with parameter 0.

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...+YN(r) X(t) Y, Y/N (1)