Let X1 denote a random sample of size 1 from a population with pdf fX(x|) = 2 e |x| , where < x < and > 0. (a) Show that Y = |X1| has an exponential distribution with parameter , ie., its pdf is fY (y|) = ey , where 0 < y < (b) Find the Uniformly Most Powerful (UMP) test based on Y of size = 0.05 for testing H0 : = 1 against H1 : = 2 (c) Obtain the power of this test. Why do you think the power of this test is so low