Problem 7 [4+3 +3 = 10 points] 08 Consider the birth-and-death process, X = {X (t): t≥ 0} with birth rates and death rates Ak=2(k+1), for k ≥0 Hk3k, for k≥ 0. 1. Derive the steady state distribution of X (t), that is for k = 0,1,... 2. Determine the limiting expectation, 3. Determine the limiting variance, lim P [X (t)=k] = 1410 lim E[X (t)]= 817 lim VAR [X (t)]= 81I