Suppose that W 1 is a random variable with mean and variance 2 1 and W 2 is a random variable with mean and variance 2 2 From Example 5 4 3, we know that cW 1 (1 c)W 2 is an unbiased estimator of for any constant c 0 If W 1 and W 2 are independent, for what value of c is the estimator cW 1 (1 c)W 2 most efficient

Question: Suppose that W 1 is a random variable with mean and variance 2 1 and W 2 is a random variable with mean

Suppose that W₁ is a random variable with mean μ and variance σ²₁ and W₂ is a random variable with mean μ and variance σ²₂. From Example 5.4.3, we know that cW₁ + (1 − c)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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