Best linear blend of two estimates

MediumRandom Variables Statistics~5m

Two independent unbiased estimators of the same quantity have variances $\sigma_1^2 = 1$ and $\sigma_2^2 = 3$ . What weight $w$ on the first estimator (and $1-w$ on the second) minimizes the variance of the blend? (to 2 decimals)

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Set the derivative of the blended variance to zero.
Weight each estimator proportionally to 1/variance.

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Best linear blend of two estimates

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