I'm looking at this page: Bernoulli Distribution -- from Wolfram MathWorld
I think I'm missing something simple, but how do you get from equation 24 to 25?
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Yes, it looks a little... nonobvious.
The easiest thing is to immediately apply the Binomial theorem: . Maybe they factored first: .
yes, just pull out the p, the rest sums to one.
Since it's an expectation of p-hat, shouldn't the first p (or all the p's) be a p-hat term?
P is a constant, usually unknow, that's why we estimate it with a random variable... p-hat and we like that p-hat is unbiased for p.
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