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  3. suppose x1; : : : ; xn is i.i.d exponential distri

Suppose X1; : : : ; Xn is i.i.d Exponential distribution with density f(xjθ) = (1/θ) *...

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Statistics

Suppose X1; : : : ; Xn is i.i.d Exponential distribution withdensity
f(xjθ) = (1/θ) * e(-x/θ); 0 ≤ x < 1; θ > 0:
(a) Find the UMVUE (the best unbiased estimator) of θ.
(b) What is the Cramer-Rao lower bound of all unbiased estimator ofall unbiased estimator
of θ. Does the estimator from (a) attain the lower bound? Justifyyour answer.
(c) What is the Cramer-Rao lower bound of all unbiased estimator ofθ^2?
3
(d) Find the UMVUE of θ2. Does this estimator attain the lowerbound in (c)?

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