Suppose that X1, X2, , Xm and Y1, Y2, , Yn are independent random samples, with...

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) Suppose that σ12 = 4, σ22 = 5.5, and m = n. Find the minimum sample sizes so that (X − Y) will be within 1 unit of (μ1 − μ2) with probability 0.95. (Round your answer up to the nearest integer.)

m = n =

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orchestra answered 1 year ago

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