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Let X1, ..., Xn be a random sample from a population with probability density function f(x) = θe−θx
, x > 0. Find the lower bound of the variance of unbiased
estimator for g(θ) = θ
Hint If X1, X2, ..., Xn is random sample from a population with probability density function f(x; θ) such that:
• T = h(x) is unbiased estimator of g(θ).
• L(θ) = Πn
i=1f(xi
; θ)
then, the lower bound of the variance of unbiased estimator, V (T), for g(θ) given by:



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