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Math Help - Poisson approximation

  1. #1
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    Poisson approximation

    For a Binomial distribution to be approximated to Poisson (law of large numbers).
    n should be big and p should be small.

    In the proof I can see why n must be big,
    but can some explain to me why must the probability be small?
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  2. #2
    MHF Contributor matheagle's Avatar
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    so that np converges to lambda
    the mean of both distributions are np and lambda, respectively
    if p didn't go to zero inversely to n, then the mean would explode and you couldn't converge
    to a distribution with a finite mean like a Poisson
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