Question: 1) Let X1, X2, ...Xn are i.i.d random sample from a Rayleigh Distribution with PDF (30 Points) . 2 exp( f (ac; 0) 20 =

1) Let X1, X2, ...Xn are i.i.d random sample from a

1) Let X1, X2, ...Xn are i.i.d random sample from a Rayleigh Distribution with PDF (30 Points) . 2 exp( f (ac; 0) 20 = 0, 0.w a) Show that X?, i = 1, 2, ..n has a gamma distribution, [(1, 20) (Hint: Use Jacobian Transformation) b) Show that the RR of the MP (Most Powerful) test for testing Ho : 0 = 60 VS H1 : 0 = 01 (>60), is En X? > c (c is any known number) c) For fixed size o, (level of significance of the test ), find the exact expression of c. (Hint: Expression of c will be a function of do and a)

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