It looks like you're placing a distribution on P.
But the n is fixed.
If all you want is.... , well that's easy.
The definition of variance is .
Let , so .
Hence
.
Hello, I am studying Variance for a binomial distribution and I am hoping if someone can help me understand where n^2 comes from.
E(Y|P) =np V(Y|P)=npq
V(Y) = E[V(Y|P)] + V[E(Y|P)]
=E(npq) +V(np) = nE[p(1-P)] + n^2V(P)