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  1. #1
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    poisson with given

    i know the poisson formula but how does a given condition affect it?

    i.e. E(X)=3, find P(X=2|X>1).

    i have X>1, as 1 - 4e^-3, and i can work out the normal P(X=2) but how does the given X>1 affect it? i dont know what to do
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    Quote Originally Posted by mathcore View Post
    i know the poisson formula but how does a given condition affect it?

    i.e. E(X)=3, find P(X=2|X>1).

    i have X>1, as 1 - 4e^-3, and i can work out the normal P(X=2) but how does the given X>1 affect it? i dont know what to do
    You're expected to understand conditional probability: \displaystyle \Pr(A | B) = \frac{\Pr(A \cap B)}{\Pr(B)}.

    Note that \Pr(X = 2 \cap X > 1) is equivalent to \Pr(X = 2) ....
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    so this will just be p(x=2)/p(x>1) then? just divide my own calculations

    i get 0.28 is thAT RIGHT
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    Quote Originally Posted by mathcore View Post
    so this will just be p(x=2)/p(x>1) then? just divide my own calculations Mr F says: Yes.

    i get 0.28 is thAT RIGHT
    If you have calculated each probability correctly and then done the arithmetic correctly then your answer will be correct.
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    yesh but thats what im asking if i did it correctly or not... is my result correct or not...?
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  6. #6
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    Quote Originally Posted by mathcore View Post
    i know the poisson formula but how does a given condition affect it?

    i.e. E(X)=3, find P(X=2|X>1).

    i have X>1, as 1 - 4e^-3, and i can work out the normal P(X=2) but how does the given X>1 affect it? i dont know what to do
    Bayes' theorem can be used here:

    P(x=2|X>1)=\dfrac{P(X>1|X=2)P(X=2)}{P(X>1)}=\dfrac  {P(X=2)}{1-(P(X=0)+P(X+1))}

    where:

    P(X=k)=\dfrac{3^ke^{-3}}{k!}

    To two significant firures this gives 0.28 which is your answer, but you should give more digits (even if they are zeros)

    CB
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