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