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Math Help - find the distribution of the sum of 25 ind poisson rv's

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    Junior Member plm2e's Avatar
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    find the distribution of the sum of 25 ind poisson rv's

    Find the distribution of the sum of 25 independent Poisson random variables with the identical parameter λ = 5
    Last edited by mr fantastic; May 1st 2009 at 07:26 AM. Reason: Restored original question
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    Moo
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    Hello,
    Quote Originally Posted by plm2e View Post
    This is confusing me and i would appreciate any help i can get.

    Find the distribution of the sum of 25 independent Poisson random variables with the identical parameter λ = 5
    Use moment generating function, by remembering that the mgf of the sum of independent rv equals the product of their mgf.

    (you should find the mgf of a Poisson distribution with parameter 25x5)
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    Junior Member plm2e's Avatar
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    ok so, Mx(t) = e^[λ((e^t)- 1))]

    i get e^[5((e^25) - 1)] = my ti 83 says overflow

    i think i may be confused on what t is
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    Junior Member plm2e's Avatar
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    missed the product part on my last post, but im still concerned about what the t means in the mgf
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    Moo
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    Quote Originally Posted by plm2e View Post
    ok so, Mx(t) = e^[λ((e^t)- 1))]

    i get e^[5((e^25) - 1)] = my ti 83 says overflow

    i think i may be confused on what t is
    Let X_1,\dots,X_{25} be iid Poisson rv with parameter 5.

    Then their mgf is : M(t)=e^{5(e^t-1)}

    The mgf of X=X_1+\dots+X_{25} is :
    M_X(t)=M_{X_1+\dots+X_{25}}(t)=M_{X_1}(t)\cdots M_{X_{25}}(t)=M(t) \cdots M(t)=[M(t)]^{25}
    =\left(e^{5(e^t-1)}\right)^{25}=e^{25 \cdot 5(e^t-1)}=e^{125(e^t-1)}

    And this is the mgf of a Poisson distribution with parameter 125.
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