2. Let X be a normal random variable with mean M); and variance 4, and let Y be a normal random variable with mean y and variance 9. Let (9 = ,uX [,Ly. Our hypotheses are - Null hypothesis H0 is 6 = 0. . Alternative hypothesis H1 is 6' > 0. Suppose that X and Y are independent. Let X and V be the sample mean for X and Y, respectively, with 72 samples for each. Suppose that we reject H0 if X Y 2 k for some undetermined k. (a) (4 points) Find the power function K09) and write it in terms of theta, n, k, and the cdf (I) of a standard normal random variable (b) (4 points) Find n and It so that these two conditions are satised: . The type-I error rate or is 5 percent, and o The type-II error rate ,6 when 9 = 2 is 10 percent