1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Relation between Gamma and Poisson

  1. Mar 14, 2012 #1
    I'm having trouble doing a classic proof (integration par part and induction on r) for this :

    Pr(X>t)=Pr(Y ≤r−1), where X follows a gamma Γ(α = r, β = 1/λ) and Y a Poisson P (λt).
    Start with r = 1 (exponential distribution).

    I dont really understand what induction on r really means.

    I tried just showing the basic density equation for both (Gamma and Poisson) but i dont know how to make them simplify into the same thing.
     
  2. jcsd
  3. Mar 15, 2012 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    First, you want to show that the statement Pr(X>t) = Pr(Y≤r-1) is true when r=1. This is the base case. Next, you assume the statement holds when r=k and show that the statement is true for r=k+1. That's what you need to do for a proof by induction.

    When r=1, what are the probability density functions for X and Y? Write down expressions for Pr(X>t) and Pr(Y≤0) and show they are equal.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook