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Let X1, X2, . . . , Xn be iid following exponential distribution with parameter λ...

Let X1, X2, . . . , Xn be iid following exponential distribution with parameter λ whose pdf is f(x|λ) = λ^(−1) exp(− x/λ), x > 0, λ > 0.

(a) With X(1) = min{X1, . . . , Xn}, find an unbiased estimator of λ, denoted it by λ(hat).

(b) Use Lehmann-Shceffee to show that ∑ Xi/n is the UMVUE of λ.

(c) By the definition of completeness of ∑ Xi or other tool(s), show that E(λ(hat) |  ∑ Xi) = ∑ Xi/n

Math   Statistics-And-Probability   
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