Let X1, X2, …., Xn, and Y1, Y2, ….Yn be 2n observations from a population with mean µ and variance σ2=1. Consider:
An = ((X1+X2+⋯.+Xn)- (Y1+Y2+⋯..+Yn))/n
Compute the mean and the variance of (√n)An
i got following
x bar - y bar approach normal (M1 - M2 , 1/n + 1/n)