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Math Help - Poisson distribution(please help if you can)

  1. #1
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    Poisson distribution(please help if you can)

    I understand the poission approximation to the binomial distribution:

    e^{\lambda}{\lambda^k \over{k!}}

    where \lambda=np=mean number of success in a given population of size n

    But I am confused how it is mapped to the Poission distribution:

    e^{\lambda t}{(\lambda t)^k \over{k!}}

    where \lambda t=mean number of success in a given population of size n

    Now, how can \lambda and \lambda t mean the same thing???
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  2. #2
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    Quote Originally Posted by chopet View Post
    Now, how can \lambda and \lambda t mean the same thing???
    Think of the Poisson variable \lambda as a rate, so you need to multiply it by a given amount of time for a mean or expected amount of outcomes in that time period.
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  3. #3
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    So we are treating the first case as t=1?

    t=2 would mean we are dealing with 2 populations?

    But the mean number per population should be independent of t right?
    If in t=1 population, the mean is 30 successes.
    Then in t=10 populations, the mean is still 30 successes.

    Is my concept wrong?

    Thanks for your help.
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