Solved – Inverse-variance weighting

I'm writing a Bachelor Thesis in engineering an a small part of it has two deal with assigning weights to independent measurements. This is from the thesis:

I am pretty sure that what equations (3.23) and (3.24) are correct, the fit my data perfectly, but I can't for the life of me find a source to confirm them. I've found two Wikipedia articles relating to them, but they don't really give any sources. Does anyone know whether what I wrote is correct, and if so, where I could find a source to cite?

For the case of two weights, you can simply set $w_2 = 1 – w_1$, plug it into (3.23) and then find the minimum of the quadratic function of $w_1$.

In general, as explained here on p 5, you have to apply the Lagrange multiplier method that will give you a closed-form solution unless you restrict the weights to be non-negative.

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