Let N(t) be a Poisson process with parameter A and X (t) is defined as follows: 1=0 X (t ) = -1) N (t) 130.(a) Find the transition matrix for X (t)? [Hint: no need to simplify any infinite sums.] (b) Consider the DTFS Markov chain Yx derived from Xt by sampling X at regular unit intervals At = 1: Yk = X(k . At). What is a stationary distribution of Y,? Is Y, ergodic