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Homework Help: Probability- Exponential Random Variables

  1. Sep 24, 2010 #1
    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) [tex]\leq[/tex] [tex]\frac{-logP[Sn >n*a]}{n}[/tex]

    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:[tex]\frac{x^(^n^-^1^)*e^(^-^x^)}{(n-1)!}[/tex]
    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
  2. jcsd
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