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Poisson variable w/ uni. dist. parameter

  1. Feb 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Let
    [itex]X\sim Poi(\lambda)[/itex]
    and assume
    [itex]\lambda\sim Uni(0,5)[/itex]

    Q: Find
    [itex]\mathbb{P}\{X \geq 3\}[/itex]


    2. Relevant equations
    For a Poisson r.v. with parameter lambda,
    [itex]\mathbb{P}\{X = k\}=\frac{\lambda^{k}e^{-\lambda}}{k!}[/itex]

    and the probability that lambda is in the interval (0,5) is 1/5 and 0 otherwise.


    3. The attempt at a solution

    I know that I first need to write out P(X<=2) and use the fact that P(X>=3)=1 - P(X<=2). However, how do I use the fact that lambda is uniform over (0,5)? I can't seem to think about it correctly.
     
    Last edited: Feb 9, 2009
  2. jcsd
  3. Feb 10, 2009 #2
    Condition on [tex]\lambda[/tex].
     
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