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Math Help - Q: Independent negative binomial random variables

  1. #1
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    Q: Independent negative binomial random variables

    I am given that X1, X2, X3,....,Xk are independent negative binomial random variables with parameters r1 and p, r2 and p,...and rk and p, respectively. I am trying to find the mgf, pdf, expected value and variance of X=X1+X2+...+Xk.

    I am fine with dealing with a single negative binomial variable, so my question is how to deal with a sum of them. Not sure really where to start.

    Thanks.
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  2. #2
    MHF Contributor matheagle's Avatar
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    Use the MGF to show that a sum of independent Neg Bi's is a Neg Bi, IF they have the same parameter p.
    That makes sense since you are are now waiting for the (r1+..+rk)'th success to occur.
    You can find the MGF on http://en.wikipedia.org/wiki/Negativ...l_distribution
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