Suppose that X1, X2,..., Xn and Y1, Y2,..., Yn are independent random samples from
Chapter 7, Problem 7.58(choose chapter or problem)
Suppose that X1, X2,..., Xn and Y1, Y2,..., Yn are independent random samples from populations with means 1 and 2 and variances 2 1 and 2 2 , respectively. Show that the random variable Un = (X Y ) (1 2) ( (2 1 + 2 2 )/n satisfies the conditions of Theorem 7.4 and thus that the distribution function of Un converges to a standard normal distribution function as n . [Hint: Consider Wi = Xi Yi , for i = 1, 2,..., n.]
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