how can I calculate the variance of p as derived from a binomial distribution? Let's say I flip n coins and get k heads. I can estimate p as k/n, but how can I calculated the variance in that estimate?
I'm interested in this so that I can control for variance in my ratio estimates when I'm comparing between points with different numbers of trials. I'm more sure of the estimate of p when n is greater, so I would like to be able to model how reliable the estimate is.
Thanks in advance!
- 40/100. The MLE of p would be 0.4, but what is the variance in p?
- 4/10. The MLE would still be 0.4, but the estimate is less reliable, so there should be more variance in p.