Let f(x Icirc cedil ) be the logistic location pdf e(z 0) F(z 0) 0ro, 0 0 8 (1 e(z 0))2

Question: Let f(x|Î¸) be the logistic location pdf e(z-0) F(z|0) = -0ro, -0 <0 <8. (1+ e(z-0))2

Let f(x|Î¸) be the logistic location pdf

(a) Show that this family has an MLR.
(b) Based on one observation, X, find the most powerful size Î± test of H0 : Î¸ = 0 versus H1: Î¸ = 1. For Î± = .2, find the size of the Type II Error.
(c) Show that the test in part (b) is UMP size Î± for testing H0: Î¸ 0. What can be said about UMP tests in general for the logistic location family?

e(z-0) F(z|0) = -0ro, -0

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