Beta Distribution Mean and Variance Proof

In this video I derive the Mean and Variance of the Beta Distribution. I also provide a shortcut formula to allow for the derivation of the moments of the Beta Distribution in a more timely manner.
The Mean and Variance of the Beta Distribution is easily derived by the realization that we can transform the Integral of the product of x with pdf into some constants multiplied by the integral over the entire support of a new Beta Distribution's pdf.
#Mean
#Variance
#Beta
0:00 Introduction: PDF and Insights
2:23 Deriving the Mean
8:15 Mean of Beta Distribution
8:30 An equation for the Moments
10:02 Deriving the second Moment
12:06 Second Moment's Formula
12:45 Deriving the Variance
14:50 Variance of Beta Distribution

[@arefcr7]

Great explanation. Thank you for this tutorial.

[@santiagolicea3814]

I think you forgot to explain that the a+1 actually comes in from multiplying the x^1 * x^(a-1) = x^(a+1)-1

[@fredynyanga1691]

Congratulations sir you so genius

[@ologunshadrach7570]

Your works are too rough bro