Suppose that X1, X2, , Xm and Y1, Y2, , Yn are independent
random samples, with the variables Xi normally distributed with
mean μ1 and variance σ12 and the variables Yi normally distributed
with mean μ2 and variance σ22. The difference between the sample
means, X − Y, is then a linear combination of m + n normally
distributed random variables and, by this theorem, is itself
normally distributed.
(a) Find E(X − Y).
(b) Find V(X − Y).
(c)...