Mathematics, 17.06.2020 18:57, jamisoncameron000

Shocks occur to a system according to a Poisson process of intensity λ. 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 bethe damage caused by the i th shock. Then X(t) = Y1+...+YN(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 Θ

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Shocks occur to a system according to a Poisson process of intensity λ. Each shock causes some damag...