5.6.2 Shocks occur to a system according to a Poisson process of intensity . 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 Yi be the damage caused by the ith shock. Then X.t/ D Y1 C


CYN.t/

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 .