Consider two independent populations with means i and 2, respectively. The variances of the populations are denoted by 1^2 and 2^2 respectively. Let Xi be the sample mean for a sample of size n; of the ith population, for i = 1.2. Use the results from section 7.2 to answer the following questions. (a) Show that X1 - X2 is an unbiased estimator of 1 - 2.

(b) Show that Var (X1 - X2) = 1^2 /n1 + 2^2/ n2.

(c) If the two populations are normal with 1 = 10 , 2 = and 1^2 = 2^2= 5, and the sample sizes are n1 = n2 = 10, give the distribution of X1 - X2 and calculate P (X1 - X2> 1.5).