Question: Q2. Let X 1, X 2 be a random sample from exponential distribution (sample of n observation) f(x 1 ; 1 ) = (1/ 1

Q2. Let X1, X2be a random sample from exponential distribution (sample of n observation)

f(x1; 1) = (1/ 1) e-(x1/ 1),x1>0.

f(x2; 2) = (1/ 2) e-(x2/ 2),x2>0.

Test the hypothesis for H0: 1= 2 (=)vs H1: 1 2.

(a). Show that the test statistic can be expressed as a function of .

(b). Show that distribution of T does not depend on

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