Given two samples X=(X1,…,Xn) and Y=(Y1,…,Yn) where Xi ~ N(mu_x, sigma_x^2) and Yi ~ N(mu_y, sigma_y^2). We want to to test H0: mu_x – mu_y = 0 vs. H1: mu_x – mu_y != 0 and we happen to know that sigma_y^2 = sigma_x^2 = 1. Derive the distribution of the statistic X_bar – Y_bar under H0.