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5. (20pt) Suppose we have two independent random samples: X1,,Xn1 is an iid sample from EXP(1) and Y1,,Yn2 is an iid sample from EXP(2). Consider Q=1Y2X (a) Prove Q is a pivotal quantity and give its distribution. (b) Use the pivot in part (a) to derive a 100(1)% confidence interval for 2/1..

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5. (20pt) Suppose we have two independent random samples: X1,,Xn1 is an iid sample from EXP(1) and Y1,,Yn2 is an iid sample from EXP(2). Consider Q=1Y2X (a) Prove Q is a pivotal quantity and give its distribution. (b) Use the pivot in part (a) to derive a 100(1)% confidence interval for 2/1.

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