Consider the shot-noise process: dxt = -axt dt + BdN/(t) where N, is a Poisson Process of rate lambda. Assume that the initial condition is uniformly distributed in the interval [0, 1]. We denote m(k)(t) = E[] the kth moment of It. (a) Write the equation on my 201) and the initial condition m(1)(0). (b) Solve this equation. (c) Let k > 2. Write the equation of m(k) in terms of m(k-1) and the initial condition m(k) (0) (d) Solve this equation using the variation of constant formula for linear differential equation. We recall that this formula indicates that the solution to a differential equation die Yu + g(t) is given by x(t) = x(0)ext + S6 g(s)ey(ts)ds. (e) Use this formula to find the variance of the shot-noise process