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?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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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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