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Question.1 (11 Marks] Let X be a random variable with the following pdf: f(x; 8) 1>0, >0. 1 (1) (a) Show that I f(x;0)d.r = 1

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oth Answer - у к». ) с hp hah oh (ве 0), ә (40) 10 dx=0 dy КО-Х. - ҒУ txe z de f(0,0) dal = 1 (1,0) = ғ) »!) os xeze (0) овок(6) The pdf. of one - Parameter exponential family is written as, 010).T(x) $(1,0) = c(0). hſx). e Given that, *1940) 1 x (%)nu 2 zn M a(t,0)= (6) SWI и Iя, я, - Comparing it with Neyman factorization Theorem . L=GCT, O). Hall 2n comparing 0 & ②, wea lo8L and & DogL 2 loge eo ao For M. L. E. of o, we must have a lose =0 gives - 20 / + 2 h et le Xi 2 n ie Exe yo ie Xi an M

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