10. Let Y₁, Y₂,..., Yn be random sample from the exponential distribution with mean Two 0 Ꮎ " estimators are proposed for 0; 0₁ = Y(1) and 02, the maximum likelihood estimator. (a) Show that both ₁ and 2 are biased estimators of 0.

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10. Let Y₁, Y₂,..., Yn be random sample from the exponential distribution with mean Two
0
estimators are proposed for 0; 0₁ = Y(1) and 02, the maximum likelihood estimator.
(a) Show that both ₁ and ₂ are biased estimators of 0.
(b) Find the estimators 03 and 04 that are respective functions of 0₁ and 02 that are unbiased.
(c) Find Var (03) and Var(0₁).
(d) For each of 03 and 4 find their efficiency in relation to the Cramer-Rao lower bound variance.
(e) A random sample available from the given population is given below:
5.354 0.851 1.116 6.556 0.171 6.642 0.104 3.227 2.419 0.587
i. Find estimates of Var (03) and Var(0₂)
ii. Find the estimate of RE(03, 04) and comment on your result.
Transcribed Image Text:10. Let Y₁, Y₂,..., Yn be random sample from the exponential distribution with mean Two 0 estimators are proposed for 0; 0₁ = Y(1) and 02, the maximum likelihood estimator. (a) Show that both ₁ and ₂ are biased estimators of 0. (b) Find the estimators 03 and 04 that are respective functions of 0₁ and 02 that are unbiased. (c) Find Var (03) and Var(0₁). (d) For each of 03 and 4 find their efficiency in relation to the Cramer-Rao lower bound variance. (e) A random sample available from the given population is given below: 5.354 0.851 1.116 6.556 0.171 6.642 0.104 3.227 2.419 0.587 i. Find estimates of Var (03) and Var(0₂) ii. Find the estimate of RE(03, 04) and comment on your result.
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