4. Suppose that A has pdf 1 = (1)f 0+1 0+ 1 (02 X e- 01 ), 1 > 0 Let r.v. NJA = ) have a Poisson distribution with parameter 1. (a) Show that PN(t) = 0+1 (t - 1) ) + A + 1 A (t - 1)) -2 (b) Determine E[N] and Var[N] (c) Show that PIN = n] = 02 ( 0 + 2 + n ) (8 + 1) (n+3) using i) pgf ii) the fact that P[N = n] = P[N1 = n]+ 4P[N2 = n], by identifying the distribu- tions of N1 and N2