# how to find the p.d.f. of n exponential distributed random variables?

• Feb 3rd 2009, 02:59 PM
silversand
how to find the p.d.f. of n exponential distributed random variables?
n exponential distributed independent random varibles .

how to find the p.d.f. of their sum?
• Feb 3rd 2009, 04:10 PM
mr fantastic
Quote:

Originally Posted by silversand
n exponential distributed independent random varibles .

how to find the p.d.f. of their sum?

I suggest using a moment generating function approach.
• Feb 22nd 2009, 10:53 PM
matheagle
Quote:

Originally Posted by silversand
n exponential distributed independent random varibles .

how to find the p.d.f. of their sum?

If each $\displaystyle X_i\sim\Gamma(1,\theta)$
and they are independent, then their sum is a $\displaystyle \Gamma(n,\theta)$
by multiplying their MGFs.
• May 4th 2009, 08:30 AM
hernanariel09
Quote:

Originally Posted by silversand
n exponential distributed independent random varibles .

how to find the p.d.f. of their sum?

As a gamma function with alpha= n and beta= beta