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?

Thanks!

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- January 19th 2011, 12:16 PMreflexBernoulli parameter expectation
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?

Thanks! - January 19th 2011, 12:48 PMemakarov
Yes, it looks a little... nonobvious.

The easiest thing is to immediately apply the Binomial theorem: . Maybe they factored first: . - January 19th 2011, 04:37 PMmatheagle
yes, just pull out the p, the rest sums to one.

- January 21st 2011, 11:25 AMreflex
Thanks!

Since it's an expectation of p-hat, shouldn't the first p (or all the p's) be a p-hat term? - January 21st 2011, 11:44 AMmatheagle
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.