Question: Consider a random phenomenon specified by the probability density function (with p known) For any random sample ( X u ...,X n) from this let

Consider a random phenomenon specified by the probability density function (with p known)

fx(x|0) = (p) 0 exp-1 if x > 0 otherwise.

For any random sample ( X u ...,X n) from this let us define X n by

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(a) Show that

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is an unbiased, consistent, sufficient estimator of 0 .

(b) Find the efficiency of the most efficient estimator of 0 .

fx(x|0) = (p) 0 exp-1 if x > 0 otherwise.

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