Solve[D[Σ log p + (mn - Σ) log(1-p) - (p-mu)^2/(2 sigma^2),p]=0,p]

Uh oh! Wolfram|Alpha doesn't run without JavaScript.

Please enable JavaScript. If you don't know how, you can find instructionshere.Once you've done that, refresh this page to start using Wolfram|Alpha.