Suppose that samples are taken from two normal populations. The first population has mean 80 and variance 81, and the second population has mean 100 and variance 100. If Ni = 9 is the size of the sample from the first population and N2 — 10 is the size of the sample from the second population, find

(a) the distribution of X\ + X2

(b) the distribution of Xi — X2

(c) P(170< X! + X2< 185)

(d) the distribution of Mi, the sample mean of the sample from the first population

(e) the distribution of M2, the sample mean of the sample from the second population

(f) the distribution of Mi + M2

(g) the distribution of Mi — M2

(h) P(Mi- M2> -25).