Thread: Algebraic help needed studying variance

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)

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

.

Thank you, I saw a proof of this on the internet and your proof is slightly different giving me another angle.