Issue with derivation of ML parameter estimation for binomial distribution

Hi, I have an issue with this step in the derivation of the ML solution to the binomial parameter estimation for p. Found here

https://www.projectrhea.org/rhea/ind...utions_OldKiwi

Why is the last term and not ?

Taking a concrete example, suppose , and

then

Right?

Would really appreciate someone telling me where, if, I am going wrong here.

Thanks in advance, MD

Re: Issue with derivation of ML parameter estimation for binomial distribution

Hey Mathsdog.

The reason for n - blah instead of n^2 - blah is that you have a total of n observations. If you have x of those observations corresponding to X = 1 then you have n - x corresponding to X = 0.