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Math Help - Help Urgent: Poisson Question

  1. #1
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    Help Urgent: Poisson Question

    Dear Friends,

    I have this there discrete stochastic vector

    P(X=x, Y=y) = \left\{ \begin{array}{cccc} \frac{1}{3} \cdot e^{-\lambda} \frac{\lambda^y}{y!} \mbox{x \in {-1,0,1} $\mathrm{and}$ y \in {0,1,\ldots}} \\ 0 \mbox{elsewhere.} \end{array}

    where \lambda>0

    My question I know that \sum_{n=0}^{\infty} e^{-\lambda} \frac{\lambda^n}{n!} = 1


    But does \sum_{n=0}^{\infty} \frac{1}{3} e^{-\lambda} \frac{\lambda^n}{n!} = 1 also do this??

    If yes this doen't this prove that

    P(X=x) = \left\{\begin{array}{ccx} \frac{1}{3} \mbox{x \in {-1,0,1}} \\ 0 & \mathrm{elsewhere.} \end{array}

    and

    P(Y=y) = \left\{ \begin{array}{cccc} e^{-\lambda} \frac{\lambda^y}{y!} \mbox{y \in {0,1,\ldots}} \\ 0 \mbox{elsewhere.} \end{array}

    are the probability functions P_x and P_y for X and Y respectively??

    Sincerely Yours and God bless You all
    Billy

    p.s. Is latex broken here? I heard that one had to use , but if I do that I get a post then build arrays error! Therefore I use . Hope thats allright.
    Last edited by Billy2007; December 5th 2006 at 11:00 AM.
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  2. #2
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    Quote Originally Posted by Billy2007 View Post

    p.s. Is latex broken here? I heard that one had to use , but if I do that I get a post then build arrays error! Therefore I use . Hope thats allright.
    I am not familar with probabilty. So I might be missing what you are saying.
    Whay can you not simple multiply by 1/3. If the infinite sum adds to 1 then 1/3 of the infinite sum adds to 1/3.

    Also the code is not[tex][/tex] it is [tex][/tex]
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    I am not familar with probabilty. So I might be missing what you are saying.
    Whay can you not simple multiply by 1/3. If the infinite sum adds to 1 then 1/3 of the infinite sum adds to 1/3.

    Also the code is not[tex][/tex] it is [tex][/tex]
    Dear Hacker and all,

    But doesn't a probability sum have to add up to 1 ??? Because if doesn't add up one? then its not a probability sum is it?

    Best Regards
    Billy
    Last edited by ThePerfectHacker; December 5th 2006 at 01:25 PM.
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