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Let X ~ Gamma(n, A) be a random variable with density All 1 .r: /\\ = 1'" eX) )\\.r . .'I' > 0. A > 0 f( . > rm 1 an} the critical region of a test at the signicance level of (r : 0.05. homeworkhelp.cc (a) itt "rat What is the sample space S, the parameter space 6) and the null parameter space (90 of the test? A - V v Plot the probability density functions for H0 and H1. Compute (10,05. A A A g_. t.' V v Compute the power of the test. a v Compute the probability of Type II error. AA Show that the test is the most powerful at level (1. Ha V Show that the test is also the uniformly most powerful (UMP) test when the alternative hypothesis is replaced with H1: A