Shot Noise Process. Suppose that shocks (or pulses) to a system occur at times that form a Poisson process with rate λ. The shock at time Tn has a magnitude Yn and this decays exponentially over time...

Shot Noise Process. Suppose that shocks (or pulses) to a system occur at times that form a Poisson process with rate λ. The shock at time Tn has a magnitude Yn and this decays exponentially over time with rate γ. Then the cumulative effect of the shocks at time t isAssume Y₁, Y₂,... are i.i.d. independent of N with mean μ and variance σ². Find expressions for the mean and variance of Z(t) in terms of μ and σ².