Choosing the best estimator
Given yield measurements $X_1,X_2,X_3$ from three independent runs of an
experiment with variance $\sigma^2$, which is the better of the two
estimators: $\hat\theta_{1}$= $\frac{X_1+X_2+X_3}{3}$,
$\hat\theta_{2}$=$\frac{X_1+2X_2+X_3}{4}$
I know that in order to find the best estimator if both are unbiased, we
are supposed to choose the one with the smallest variance. I need help
just starting this problem. Thank you.
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