Let X and Y be two independent and normally distributed rand

Let X and Y be two independent and normally distributed random variables with means equal to 2 and 3 and variances equal to 9 and 1 respectively. Let (X_1 X_2, X_3, X_4, X_5, X_6, X_7, X_8 X_9) and (Y_l, Y_2, Y_3, Y_4) be two independent random samples drawn from X and Y respectively. Moreover, let X and Y be the sample means and S_x_2 and S_y_2 be the sample variances of the two samples.