Problem 2. (20 Points) Let X1, ..., Xn, Yl, ..., Yn, and Wl, ..., Wn be three random samples of size nx, ny, and nw respectively. Let them be drawn from the three independent normal distributions N(ux, ox), N(uy, of), and N(uw, ow), respectively, such that: ow W~ N ( HW , X~ N(ux, O X ) Y ~ N ( MY , nw nx ny Build a confidence interval for the unknown difference ux - My - uw, assuming that the variances Ox, of, and ox are known