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?

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- Oct 12th 2009, 03:00 PMpengchao1024how 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? - Oct 12th 2009, 03:57 PMmr fantastic
- Oct 12th 2009, 07:03 PMmatheagle
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 - Oct 13th 2009, 09:09 AMpengchao1024ok
how can u find the density function of Gamma distribution by using convolution?

- Oct 13th 2009, 09:11 AMmatheagle
- Oct 13th 2009, 09:12 AMpengchao1024ok
well, would you do it like first two variables for example to show the ideas of using induction