Let Y1 and Y2 be two indepent unbiased estimators of . Assume that the variance of Y1 is twice the variance of Y2. Find the constants k1 and k2 so that k1Y1+k2Y2 is an unbiased estimator with smallest possible variance for such a linear combination.

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So Var I have

(Y1)=2Var(Y2), E(Y1)=E(Y2)=

E[(k1Y1+k2Y2)]= --> k1+k2= --> k1+k2=1

I dont know what to do next.

Can anyone help?

Thanks.