Need a little help here on this question on my problem set:

You plan to use a sample of size n to estimate an unkown paramater X whih describes some property of a population. Suppose that D1 and D2 are unbiased and consistent estimators of X. Let D3 be a new estimator which is obtained by taking a weighted average of D1 and D2, with exactly one quarter of the weight placed on D1

a. Is D3 an unbiased estimator of X? Why or Why Not?

b. Is D3 a consistent estimator of X? Why or why not?

c. Suppose D1 and D2 are efficient unbiased estimators of X. In other words, D1 and D2 both have the lowest variance among all unbiased estimators of X. Must D3 also be an efficient unbiased estimator of X? Why or Why not?

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For a.) I'm pretty sure that putting a weight on D1 would change X, and unbiased means that E(D1) = E(D2) = X. So changing the weight on D1, I'm pretty sure E(D3) /= X

I'm kind of lost after that....

Man, I thought I would be able to help you out. Then I read your question, got lost, realized my class is actually Social Science Statistics and thanked god I go to a liberal arts college Good luck!

Don't ask me, I was on the internet during prob and stats. What a horribly boring subject.

Don't ask me, I was on the internet PORN

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