Question

In: Statistics and Probability

Suppose we have a random sample of size 2𝑛 from a population denoted by 𝑋, and 𝐸(𝑋) = 𝜇 and 𝑉(𝑋) = 𝜎^2 . Let

Suppose we have a random sample of size 2𝑛 from a population denoted by 𝑋, and 𝐸(𝑋) = 𝜇 and 𝑉(𝑋) = 𝜎² . Let

be two estimators of 𝜇. Which is the better estimator of 𝜇? Explain your choice.

Expert Solution

Solution

Suppose we have a random sample of size 2𝑛 from a population denoted by 𝑋, and 𝐸(𝑋) = 𝜇 and 𝑉(𝑋) = 𝜎² .

be two estimators of 𝜇. Which is the better estimator of 𝜇? Explain your choice

Then we have

Then follow by

These two estimators are unbiased. and we have some quation

These two estimators are unbiased.

Therefore:

SUN BUNRA answered 2 years ago

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Question

Suppose we have a random sample of size 2𝑛 from a population denoted by 𝑋, and 𝐸(𝑋) = 𝜇 and 𝑉(𝑋) = 𝜎^2 . Let

Solutions

Expert Solution

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