The estimation of overall variance for fixed meta-analysis model via maximum likelihood method

[TomHsiung]

Hi, guys

I just failed to prove the way to derive the overall variance formula for fixed-effect model of a meta-analysis. By partial derivation the Log(likelihood function) of a fixed-effect model, it is easy to derive the formula for estimating the overall mean. However, I don't understand how the formula for estimating the overall variance comes from. Your help would be much appreciated. Thanks.

Tom