Let {N(t), t>0} be a Poisson process with rate (t)= e^-t. Let (Y_n)_n be a sequence of independent and identically distributed random variables with density f(y) = e^(-y+theta), for y > theta and theta > 0. For all n >= 1, Y_n id independent of the process {N(t), t>0}.
a) Compute the mean and variance of Y_1
b) If X(t) = , find the expectation of X(t)
c) Find the limit