# Homework Help: Probability- Exponential Random Variables

1. Sep 24, 2010

### Roni1985

1. The problem statement, all variables and given/known data

Suppose X1,X2.... are iid mean 1 exponential random variables. Use large deviation methodology to give a lower bound for the rate function R(a) for a>1

2. Relevant equations

R(a) $$\leq$$ $$\frac{-logP[Sn >n*a]}{n}$$

3. The attempt at a solution

I know that a sum of exponential random variables is Gamma (n, 1).

I'm having a problem with finding the probability.

the pdf of a gamma dist random variable is:$$\frac{x^(^n^-^1^)*e^(^-^x^)}{(n-1)!}$$
I think after transforming it, this is the pdf.

But I'm getting a very hard integral and even my TI-89 can't solve it.
I think I'm doing something wrong.

Last edited: Sep 24, 2010