22 - Beta conjugate to Binomial and Bernoulli likelihoods - full proof 2

This video provides a full proof of the fact that a Beta distribution is conjugate to both Binomial and Bernoulli likelihoods.
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[@yuchenwang4537]

It's very clear! Thank you. Please keep posting these tutorials😃

[@lemyul]

I don't understand but i hope my inner consciousness do

[@jacobmoore8734]

Yeah I got nuked by this ... edit: After doing some reading, I realized that *all we need to do* is a bit of reverse engineering. If we can coerce the prior*likelihood into taking the same shape as the Beta's numerator, we can reverse engineer what the denominator will be. All we need to do is factor out all constants (or integral(s) that evaluate to constants) and label it as the "denominator" and realize that (A) if the numerator takes the shape of a Beta numerator, then (B) the denominator *must* take the shape of the Beta denominator. At this point, we entirely give up on analytically solving it whatsoever. We just reverse engineer what the denominator should be given A and B above. This holds for all conjugate priors. I had to think about this for quite a while before it clicked.

[@adriaanaylsworth263]

Where did the N choose X part go though?