The random sample X1, . . . , Xn is generated from a Normal population
distribution. It is known that E(Xi) = 0, V (Xi) = σ
2
. Consider the
following point estimators of σ
2
.
(a) T1(X1, . . . , Xn) = 1
n
Pn
i=1 X2
i
(b) T2(X1, . . . , Xn) = 1
n−1
Pn
i=1(Xi − Xn)
2
In MSE sense, which is better ? (Assume that if Y ∼ χ
2
n
, then V (Y ) = 2n)
Answers
i=1 X2
i
(b) T2(X1, . . . , Xn) = 1
n−1
Pn
Answer:
ion:
The random sample X1, . . . , Xn is generated from a Normal population
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Explanatdistributio
n. It is known that E(Xi) = 0, V (Xi) = σ
2
. Consider the
following point estimators of σ
2
.
(a) T1(X1, . . . , Xn) = 1
n
Pn i=1(Xi − Xn)
2
In MSE sense, which is better ? (Assume that if Y ∼ χ
2
n
, then V (Y ) =