(6) Let X1, ..., X, be a random sample from an exponential distribution with density function f(x|0) = 0 exp[-0x), where

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6 Let X1 X Be A Random Sample From An Exponential Distribution With Density Function F X 0 0 Exp 0x Where 1 (83.14 KiB) Viewed 43 times

(6) Let X1, ..., X, be a random sample from an exponential distribution with density function f(x|0) = 0 exp[-0x), where 0 > 0. (a) Show that the critical region of a 1 test of Ho : 0 = , versus H1 : 0 + 0, is of the form C = {Xe-658 < c}. Use the central limit theorem (and R) to estimate c for a test of size 0.05 when n = 10 and 0o = 1. (b) Show that the critical region of a generalised likelihood test for this problem has the same form and use Wilks' Theorem to estimate c.