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pected value [tex]\mu[/tex] and variance [tex]\sigma^2[/tex]: Consider the class of linear estimators of the form

[tex]\mu\widehat{}[/tex] = a1X1 + a2X2 + ... + anXn (1)

for the parameter [tex]\mu[/tex], where a1, a2, ... an are arbitrary constants.

a) Find the expected value of the estimator [tex]\mu[/tex].

b) Find the variance of this estimator.

c) When is [tex]\mu\widehat{}[/tex] an unbiased estimator of [tex]\mu[/tex]?

d) Among all linear unbiased estimators of the above form (1), find the minimum

variance estimator.

Hint: Use the Cauchy-Schwarz inequality

e) What is the variance of the best unbiased estimator of the form (1)?

I am really lost and confused.

for (a) I got expected value is X1+X2+...Xn / n, is this correct or do i need to include the arbitrary constants? I thought about it again and got something totally different: i summed up a1EX1 + a2EX2 + anEXn, and wrote a general formula for it as aiEXi

for (b) is the variance just Var(miu hat) = sigma^2 (n summation (i=1) ai^2)

for (c) When Cramer-Rao inequality is satisifed?

I have not attempted (d) or (e) yet as I want to confirm that I am on the right track for (a) (b) and (c) for which I think I'm not.