# Resolved: How the variance is calculated

In the video it says that the formula of the variance has been presented before, but I can't find references. I don't understand what to replace in E(y squared), while it is clear that E(y) squared is (np)squared

Hey Davide,

Thank you for your question!

Since the expected values are a bit more cumbersome to work with, we have given an expression for the variance in terms of the probability and number of trials, namely

n.p.(1-p)

We have decided to skip the derivation of the formula but you are very welcome to give it a try yourself!

Kind regards,

365 Hristina

Thanks i'll give it a try :) but sincerly i don't know how to replace the first term of the expression :(

Hey Davide,

The trouble is that, unfortunately, the derivation is not as trivial. There is a nice proofwiki page on the topic. This page shows the derivation of E(X) for a binomial distribution, namely

E(X) = np

I think that Proof 1 would be easier to follow as it uses the formula for P(X) introduced in the video.

This page shows the derivation of E(X^2) which is even less pleasant to look at :) At the end of the day, one obtains

E(X^2) = n^2*p^2 + np(1-p)

Again, Proof 1 should be easier to follow.

It is now straightforward to obtain the result in the video lecture:

sigma^2 = E(X^2) - E(X)^2 = np(1-p)

Hope that you will find the resources helpful!

Kind regards,

365 Hristina