Suppose that W1 is a random variable with mean μ and variance σ21 and W2 is a random variable with mean μ and variance σ2. From

Question

3 years ago

14

Suppose that W1 is a random variable with mean μ and variance σ21 and W2 is a random variable with mean μ and variance σ2. 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?

Mathematics

1 answer:

vivado [14] · Answer 1 · 2022-03-12T10:58:23+03:00

Answer:

Step-by-step explanation:

The concept of variance in random variable is applied in solving for the value of c for the estimator cW1 + (1 − c)W2 to be most efficient. Appropriate differentiation of the estimator with respect to c will give the value of c when the result is at minimum.

The detailed analysis and step by step approach is as shown in the attachment.