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?

http://en.wikipedia.org/wiki/Inverse-variance_weighting

http://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Dealing_with_variance

**Contents**hide

#### Best Answer

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.

### Similar Posts:

- Solved – Measuring correlation or dependence between two data sets
- Solved – Other ways to find line of “best” fit
- Solved – Is the understanding of how to calculate the reachability distance in local outlier factor correct
- Solved – Difference of notation between cross entropy and joint entropy
- Solved – What are the key statistical concepts that relate to data mining