question about variance?

Question

Prove that <(n - )^2> = - ^2

Answer 1

<> is expectation I take it. I like En better

E(n-En)^2
= E[n^2-2nEn+E^2n]
= En^2 -2En*En+E^2n
= En^2 -E^2n


En^2 means E(n^2)
E^2n means (En)^2

Answer 2

That's not much of a question. You really just need to expand the quadratic and use the properties of expectation to get the result. In particular, expectation is a linear operation:

E(aX) = aE(X)
and
E(X+Y) = E(X) + E(Y)

Go ahead, do it. Every statistics student must do this.