# Thread: Proving Beta Distribution Variance

1. ## Proving Beta Distribution Variance

Hi, I need help to proof the Variance for Beta Distribution. I know that I am required to use the Moment generating function to solve this. However, I'm having a hard time deriving it from the beta distribution function itself. How do you get the moment generating function from the beta distribution function? And to obtain the derivative of the m.g.f to find the expected value (so that i can use it to find the variance), how exactly do you obtain it? I'm having a hard time trying to figure this out. Please help, thanks.

2. Originally Posted by jordanq
Hi, I need help to proof the Variance for Beta Distribution. I know that I am required to use the Moment generating function to solve this. However, I'm having a hard time deriving it from the beta distribution function itself. How do you get the moment generating function from the beta distribution function? And to obtain the derivative of the m.g.f to find the expected value (so that i can use it to find the variance), how exactly do you obtain it? I'm having a hard time trying to figure this out. Please help, thanks.
Are you certain you have to derive the moment generating function and then use it to get the variance?

I think it will be easier to calculate $\displaystyle E(X)$ and $\displaystyle E(X^2)$ directly from the pdf.

And if the parameters are integers then things are even easier (which is not to say that the calculation itself is easy).