- 5 Consider X To Be A Random Variable With Density Function So X 20x 1 0 0 X 1 101 1 A Show That The Distributi 1 (26.35 KiB) Viewed 63 times
5) Consider X to be a random variable with density function: So(x) = 20x +1 -0; 0<x<1, 101<1 a) Show that the distribution has MLR property with T(x) = f(!) and suggest a MP a- size test for Ho : 0 = 66 against H : 0 = 4, (0, >) and the power of test. b) Extend your result to Ho : f() = 0f(x)+(1-0) 12(x) against H, : (1-0) f(x)+ 012(r) where and 12 are both density functions c) Can we extend the test to Ho : 0 <0. against H:> If your answer is no prove it. if your answer is yes find the test and its power. d) Extend you work in (a) for fo(x) = 2(1 - 0)x +0; 0<x<1, 10 <1 (25 points)