Thread: how to show their sum is another distribution

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?

Originally Posted by pengchao1024

give me a hint guys:

Xi iid some known distribution, how to show their sum is another distribution
i just want a hint on what to do to show that.

More details would help.

Use the product of the MGFs.
The sum of INDEPENDENT gamma's with the same BETA

So if then



That's also how you prove the sum of independent chi-squares is a .

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

how can u find the density function of Gamma distribution by using convolution?

Originally Posted by pengchao1024

how can u find the density function of Gamma distribution by using convolution?

painfully, that's an n-fold integral

well, would you do it like first two variables for example to show the ideas of using induction