6.

(Extra Credit 10 points) Let the random variable X be an observation from an exponential distribution with known -0x parameter @, i.e., fy(x) = {96' , x=0 0, x 0,): HOZ B = 90 H1: 0 = 91 (a) Assuming that the prior probabilities, P(H,) and P(H,) are equally likely, determine the statistical test to decide between H, and H;. (b) Find the power of the test