Xi idd exponential distribution, show sum of n Xi is gamma distribution.
i think this is typical question. but i got no idea at all. So you try to show p.d.f.? or other ways?
Xi idd exponential distribution, show sum of n Xi is gamma distribution.
i think this is typical question. but i got no idea at all. So you try to show p.d.f.? or other ways?
Use the product of the MGFs.
The sum of INDEPENDENT gamma's with the same BETA
So if $\displaystyle X_i\sim\Gamma (\alpha_i, \beta)$ then
$\displaystyle \sum_{i=1}^nX_i\sim\Gamma (\sum_{i=1}^n\alpha_i, \beta)$
That's also how you prove the sum of independent chi-squares is a $\displaystyle \chi^2$.
You just add the dfs.
BUT you need independence.
I'm working on a random stopping boot strap problem where the chi-squares are NOT independent.
Anyone want to help me? lol