Stochastic processes;

1. Let T and U be independent random variables with Erlang(1, 1) distri- bution. We define two stochastic processes X, t ( [0, too) and Y, te [0, too) with the following formulas 0 if t = [0, U), X= if t = [0. T), Y= 0 if t > T; if t > U. (a) For t 2 0 find the distribution of X, and Y. (b) Verify if X and Y are distinguishable. 2. Let Net ( [0, too) be a Poisson process with intensity A = 2. Find two-dimensional distributions of N, i.e. for any 0 -2) the following SDE: dY = dt + 2\\YdB, with the initial condition Yo = 4