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Math Help - poisson distribution

  1. #1
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    poisson distribution

    Is there an intuitive way to explain the forumla P(X=x)=\frac{e^{-\mu}\mu^x}{x!} ?

    For example in the binomial distribution with n trials & probability of sucess p you can see that to get r sucesses you must also have n-r failures and the trials are independent so this probability is p^r x (1-p)^n-r, and then you don't care about the order so that's where the n choose r comes in...

    But is there a way to explain the poisson formula? Where did it come from?
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  2. #2
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    Quote Originally Posted by HD09 View Post
    Is there an intuitive way to explain the forumla P(X=x)=\frac{e^{-\mu}\mu^x}{x!} ?

    For example in the binomial distribution with n trials & probability of sucess p you can see that to get r sucesses you must also have n-r failures and the trials are independent so this probability is p^r x (1-p)^n-r, and then you don't care about the order so that's where the n choose r comes in...

    But is there a way to explain the poisson formula? Where did it come from?
    http://www.uoxray.uoregon.edu/ph353/...stribution.pdf
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