Pls provide steps

Let {X1, X2, ..., Xn} be a random sample from n(Hx, ox), and {Y1, Y2, ..., Ym) be a random sample from n (My, Ov ). Assume that the two random samples are independent. Denote (X - Y) - (HX - MY) (n - 1)$2 (m - 1)s U = and V = + XN ox OY + n m (a) If U and V are independent, "X = d, and d is a known constant, construct a random variable W which has a t distribution. Hint: Show that (n - 1)$2 (m - 1)sz V = + doy ~Xm+n-2 (b) Using W, construct a 1 - a confidence interval for Mx - Hy. Hint: P (-ta antm-2