Question: 1) Let X : (X1,X2, . . . ,Xn) be a sample of n observations each with a uniform in [0, (9) density 10 0

1) Let X : (X1,X2, . . . ,Xn) be a sample of n observations each with a uniform in [0, (9) density 10 0 is an unknown parameter. Denote the joint density by L(X, t9). c) Find the power function of the test and sketch the graph of Egg?\" as accurately as possible.| 7 E d) Show that the random variable Yn : n(1 9 ) converges in distribution to the exponential distribution With mean 1 as n > 00. Hence justify that X0!) is a consistent estimator of 19

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