Question 1: (15 Total Marks) Indicate which option correctly completes the given statement. [2.5 marks each] a) If two independent random variables, X and Y, have distributions with cgfs kx(t) and ky(t), respectively, then the distribution of Z = X - Y has cof (1) kz (t) = kx (t) + ky ( -t); (2) kz (t) = kx (t)/ky (t); (3) kz(t) = kx(t) - ky(t). b) If N ~ NB(18,0.75) and X1, X2, ... are iid random variables independent of N, then the random sum S = =1 X; and the fixed sum T = El, X; will satisfy: Var(S) > Var(T) (1) Always; (2) Only if IE(X;)| 2 SD(X;); (3) Only if |E(X;) |