How do you find the mean and variance of part(d)?I need the detailed solution.

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How do you find the mean and variance of part(d)?I need the detailed solution.

2. Suppose X1, X2, X3 denote a random sample from exponential distribution with mean 0. Find
all unbiased estimators among the following five estimators.
(a) 01 = X1
(b) Ô2 = X1+X2
(c) Ôg = X1+2X2
(d) Ô4 = min{X1, X2, X3}
(e) Ôs = X
3
%3D
%3D
Among all unbiased estimators which has the smallest variance?
Transcribed Image Text:2. Suppose X1, X2, X3 denote a random sample from exponential distribution with mean 0. Find all unbiased estimators among the following five estimators. (a) 01 = X1 (b) Ô2 = X1+X2 (c) Ôg = X1+2X2 (d) Ô4 = min{X1, X2, X3} (e) Ôs = X 3 %3D %3D Among all unbiased estimators which has the smallest variance?
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