Work out the variance of the gamma

[gerv13]

Hi, I'm trying to work out the variance of the gamma(I'm up the the part where you multiply $$x^2$$ by the function), but i don't know how to work out what

$$\gamma(\alpha + 2)$$ equals to

i know I am supposed to use the fact that $$\gamma(\alpha + 1) = \alpha \gamma(\alpha)$$

but i don't understand what to do, please help

 

[HallsofIvy]

It's not clear whether you are talking about the gamma probability distribution or the gamma function. The gamma function has the property that $\Gamma(\alpha+1)= \alpha\Gamma(\alpha)$ but is normally represented by the capital $\Gamma$, not $\gamma$.

In any case, $\Gamma(\alpha+ 2)= \Gamma(\alpha+1+ 1)$$= (\alpha+1)\Gamma(\alpha+1)= (\alpha+ 1)\alpha\Gamma(\alpha)$.

 

[tickle_monste]

It's not clear whether you are talking about the gamma probability distribution or the gamma function.

Hi, I'm trying to work out the variance of the gamma

I'm not sure either, but I have to guess its the probability distribution.

 

[gerv13]

yupp i actually meant $$\Gamma$$ sorry about that. but thanks for the help