Consider a random sample X1,..., Xn with n> 3 from the exponential distribution with parameter > 0 and density f(x;A) = e-=/A, z>0. Consider the following two estimators of A: 3 X;, Ã =nX(1). 3 i=1

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Construct an estimator which improves on A (you do not need to have a closed
form for it, but you do need to prove that it is an estimator).
Transcribed Image Text:Construct an estimator which improves on A (you do not need to have a closed form for it, but you do need to prove that it is an estimator).
Consider a random sample X1,..., X, with n > 3 from the exponential distribution
with parameter 1 > 0 and density
f(x; A) = e-=/A,
x > 0.
Consider the following two estimators of A:
3
EXi, Ã =nX(1).
i=1
Transcribed Image Text:Consider a random sample X1,..., X, with n > 3 from the exponential distribution with parameter 1 > 0 and density f(x; A) = e-=/A, x > 0. Consider the following two estimators of A: 3 EXi, Ã =nX(1). i=1
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