Suppose that Y₁, Y2, Y3 denote a random sample from an exponential distribution with density function 1 f(y) = =-e-³, y>0, 0>0 Y₁+Y₂ Y₁+2Y₂, ₁ = Y(1) Five estimators are proposed for the parameter 0, Ô₁ = Y₁, Ô₂ = · and  =Ÿ 2 3 2,03 =

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5. Suppose that Y₁, Y2, Y3 denote a random sample from an exponential distribution with density
function
1
f(y) == e 6, y> 0, 00
Y₁ + 2Y₂
Five estimators are proposed for the parameter 0, Ô₁ = Y₁, 0₂:
Y₁+Y₂
03
2
=
Ô₁ = Y(1)
=
"
3
and Ô5 = Y
(a) Compute the bias of each estimator and hence identify the unbiased estimators.
(b) Find for each of the estimators, the mean square error and hence the standard error.
(c) Find the efficiency of 85 relative to each of the other four estimators and comment on your
results.
Transcribed Image Text:5. Suppose that Y₁, Y2, Y3 denote a random sample from an exponential distribution with density function 1 f(y) == e 6, y> 0, 00 Y₁ + 2Y₂ Five estimators are proposed for the parameter 0, Ô₁ = Y₁, 0₂: Y₁+Y₂ 03 2 = Ô₁ = Y(1) = " 3 and Ô5 = Y (a) Compute the bias of each estimator and hence identify the unbiased estimators. (b) Find for each of the estimators, the mean square error and hence the standard error. (c) Find the efficiency of 85 relative to each of the other four estimators and comment on your results.
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