1. Suppose that Y is a random sample of size 1 from a population with density 63,94, 03 3,3 1 f(yl9)= {0 , elsewhere where 9 > 0. (a) Sketch the power function of the test with the critical region Y > .5. (b) Find the LRT test for testing H016 = 1 versus H1 :6 = 2 of size a. 2. Suppose that we have two independent binomial random variables X N Binomial (n,px) / (a) Find the MLE for 3) under the assumption that p = pa: = py. and Y N Binomial (m,py). (b) Find the log likelihood ratio , A, for testing H0 1132 = pg vs. HQ 519; = py. (0) Evaluate the value of this statistic if n = 378 , X = 95, m = 432, and Y = 123 . Decide whether we should reject the null hypothesis at 0.05 level. 3. Suppose that X1, X2, . . . , X\" form a random sample from the uniform distribution on the interval (0,6), and that the following hypotheses are to be tested : H0:622vs.H1:6