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6. Let X], Xy .. .Xp, be a random sample of size n, from N(#1,7), both parameters unknown. Also, let Y, Y2. ... . Y,, be another (independent) random sample of size n, from N(us, 0?), both unknown. Assuming of =07, derive the result that (1 - X2) - ta/2v S (X1 - X2) + to/1.V where V=1+n2 -2 and $2 - Wi-fi+(,-1)5: n+ny-2 is a (1 - @)100% CI estimator for A] - 2. (Note that a pivot was already derived in Chapter 1. Just use this result.)