If Y1, Y2,..., Yn denote a random sample from an exponential distribution with mean

Chapter 8, Problem 8.36

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QUESTION:

If Y1, Y2,..., Yn denote a random sample from an exponential distribution with mean , then E(Yi) = and V(Yi) = 2. Thus, E(Y ) = and V(Y ) = 2/n, or Y = /n. Suggest an unbiased estimator for and provide an estimate for the standard error of your estimator

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QUESTION:

If Y1, Y2,..., Yn denote a random sample from an exponential distribution with mean , then E(Yi) = and V(Yi) = 2. Thus, E(Y ) = and V(Y ) = 2/n, or Y = /n. Suggest an unbiased estimator for and provide an estimate for the standard error of your estimator

ANSWER:

Step 1 of 3

Given that,

If  denote a random sample from an exponential distribution with mean , then and. Thus , and  or  .

It is required to suggest an unbiased estimator for  and provide an estimate for the standard error of your estimator.

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