2019-01-23[Stay Sharp]The beta distribution is normalized

The beta distribution is distribution of probabilities.

where the is the gamma function：

It's normalized

verification:
to verify it's normalized, i.e.

so,

that's what we want to derive.

so, the beta distribution is normalized.

Ref

https://stats.stackexchange.com/questions/47771/what-is-the-intuition-behind-beta-distribution

http://rads.stackoverflow.com/amzn/click/0387310738