Suppose that W 1 is a random variable with mean μ and variance σ 1 2 and W 2 is a random variable with mean μ and variance σ 2 2 . From Example 5.4.3, we know that c W 1 + ( 1 − c ) W 2 is an unbiased estimator of μ for any constant c > 0 . If W 1 and W 2 are independent, for what value of c is the estimator c W 1 + ( 1 − c ) W 2 most efficient?
Suppose that W 1 is a random variable with mean μ and variance σ 1 2 and W 2 is a random variable with mean μ and variance σ 2 2 . From Example 5.4.3, we know that c W 1 + ( 1 − c ) W 2 is an unbiased estimator of μ for any constant c > 0 . If W 1 and W 2 are independent, for what value of c is the estimator c W 1 + ( 1 − c ) W 2 most efficient?
Solution Summary: The author explains that the value of c is the estimator w_1+(1-c)W2 most efficient.
Suppose that
W
1
is a random variable with mean
μ
and variance
σ
1
2
and
W
2
is a random variable with mean
μ
and variance
σ
2
2
. From Example 5.4.3, we know that
c
W
1
+
(
1
−
c
)
W
2
is an unbiased estimator of
μ
for any constant
c
>
0
. If
W
1
and
W
2
are independent, for what value of
c
is the estimator
c
W
1
+
(
1
−
c
)
W
2
most efficient?
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