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Probability - Poisson Probability

  1. Feb 27, 2013 #1
    1. The problem statement, all variables and given/known data

    Show that the Poisson probabilities [itex] p_{0}p_{1},... [/itex]can be estimated recursively by [itex] p_{0} = e^{-\lambda} [/itex] and

    [itex]
    p_{k}=(\lambda/k)*p_{k-1} [/itex] k=1,2,...


    2. Relevant equations

    I know the Poisson distribution [itex] f(x, \lambda) = e^{-\lambda}\lambda^{x}/x! [/itex]

    But I haven't the faintest idea what is even being asked for here. It was never covered in class, our book, or any of the books I've looked through.

    -Dave K
     
  2. jcsd
  3. Feb 27, 2013 #2

    I like Serena

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    Homework Helper

    Hi dkotschessaa! :smile:

    ##p_k## is just another way to write ##f(k, λ)##.
    What is ##f(0, λ)##?
    Can you express ##f(k, λ)## in terms of ##f(k-1, λ)##?
     
  4. Feb 28, 2013 #3
    Thank you, that was extremely helpful . I was also able to use this to get a value for P(X≤4) which was the next part of the question!

    Regard,

    Dave K
     
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