does anyone know how to find the expected value for the beta distribution?

Question

i've been at it for ages and can't seem to find an answer! i know i'm suppose to integrate the pdf multiplied by x but the integration doesn't work out so i'm guessing i should put the variable equal to something and then integtrate that!! i would be really grateful for any suggestions!!

Answer 1

If X has a Beta(a,b) distribution, its expected value is a/(a+b).

To do the calculation, note that the product being integrated is like the PDF of another beta distribution (with a different a and b). That means that if you multiply by a constant, it must integrate to one.