Could anyone help with this?

If1,X2, andX3 constitute a random sample of sizeXn=3 from a normal population with the mean m and the variance s2, find the efficiency of (1+2X2+X4)/4 relative to (X1+X2+X3)/3.X

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- Nov 2nd 2008, 11:06 AMmath beginnerEfficiency
Could anyone help with this?

If1,*X*2, and*X*3 constitute a random sample of size*X**n*=3 from a normal population with the mean m and the variance s2, find the efficiency of (1+2*X*2+*X*4)/4 relative to (*X*1+*X*2+*X*3)/3.*X* - Nov 2nd 2008, 11:18 PMCaptainBlack
$\displaystyle T_1=(X_1+2X_2+X_3)/4$ and $\displaystyle T_2=(X_1+X_2+X_3)/3$ are unbiased estimators for \mu. (As can be seen since $\displaystyle E(T_1)=\mu$ and $\displaystyle E(T_2)=\mu$ )

Then the relative efficiency $\displaystyle e(T_1,T_2)$ of $\displaystyle T_1$ and $\displaystyle T_2$ is:

$\displaystyle e(T_1,T_2)=\frac{E((T_2-\mu)^2)}{E((T_1-\mu)^2)}$

CB