2. (30 points) Suppose that Y1, . . . ,Yn is a random sample from a population whose density function is 2 3 3y y Kyle) = W exp {63} provided y 2 0 where 6 > 0 is a parameter. Note that if Y N f(y|0), then lE(Y3) = 93. (a) Verify that f (y|6) belongs to an exponential family in traditional form. (b) Determine the likelihood function L(9) for this random sample. (c) Show that the maximum likelihood estimator of (9 is 1 n 1/3 (9 = Y3 . You may use any method that we discussed in class for nding the MLE. ((1) Find the Fisher information I (0) in a single observation from this density. (e) Using the standard normal approximation for the distribution of a maximum likelihood estimator based on the Fisher information, construct an approximate 95% condence interval for 0. Note that 20025 = 1.96