5.4.22. Suppose that W₁ is a random variable with mean μ and variance σ² and W₂ is a random variable with mean μ and variance 022. From Example 5.4.3, we know that CW1 (1c)W2 is an unbiased estimator of µ for any constant c > 0. If W₁ and W₂ are independent, for what value of c is the estimator cW₁ + (1 - c)W₂ most efficient?

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5.4.22. Suppose that W₁ is a random variable with mean
μ and variance σ² and W₂ is a random variable with mean
μ and variance 022. From Example 5.4.3, we know that
CW1 (1c)W2 is an unbiased estimator of µ for any
constant c > 0. If W₁ and W₂ are independent, for what
value of c is the estimator cW₁ + (1 - c)W₂ most efficient?
Transcribed Image Text:5.4.22. Suppose that W₁ is a random variable with mean μ and variance σ² and W₂ is a random variable with mean μ and variance 022. From Example 5.4.3, we know that CW1 (1c)W2 is an unbiased estimator of µ for any constant c > 0. If W₁ and W₂ are independent, for what value of c is the estimator cW₁ + (1 - c)W₂ most efficient?
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