2. Suppose that x1, x2,..., In is a random sample drawn from a population whose density function is distributed as Exponential (VA). Suppose two possible esti- mators of A as 1 n ÂA = and AB= 2n i=1 1 n(n + 1) 2 (Σ=)² f ==— e J N (a) Are the two estimators are unbiased? Then, compute the MSE of each estimator. (b) Can you make an optimality statement about any of the proposed estima- tors Based on CRLB. What happens if n→ ∞o?

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2. Suppose that x1, x2,..., In is a random sample drawn from a population whose
density function is distributed as Exponential (VA). Suppose two possible esti-
mators of A as
1
n
ÂA
=
and AB=
2n
i=1
1
n(n + 1)
2
(Σ=)² f ==— e J N
(a) Are the two estimators are unbiased? Then, compute the MSE of each
estimator.
(b) Can you make an optimality statement about any of the proposed estima-
tors Based on CRLB. What happens if n→ ∞o?
Transcribed Image Text:2. Suppose that x1, x2,..., In is a random sample drawn from a population whose density function is distributed as Exponential (VA). Suppose two possible esti- mators of A as 1 n ÂA = and AB= 2n i=1 1 n(n + 1) 2 (Σ=)² f ==— e J N (a) Are the two estimators are unbiased? Then, compute the MSE of each estimator. (b) Can you make an optimality statement about any of the proposed estima- tors Based on CRLB. What happens if n→ ∞o?
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