5. [20 points] Let X1,..., Xn be a random sample from the distribution 0 f(x | 0) = x > 0, (1+x)1+0 for parameter 0 > 0. I (a) Write this distribution in exponential family form and find a complete statistic. (b) Does this distribution exhibit the monotone likelihood ratio property? If so, in what direction? (c) Apply the Karlin-Rubin Theorem to find the form of the rejection region for the hypotheses Ho: 000 vs H: 0>00. (d) Show that the distribution of Ti = log(1 + X) is Exp(0). - (e) Using (d), provide the threshold value to in terms of a x2 distibution for an appropriately chosen v.