# Thread: Q: Independent negative binomial random variables

1. ## 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.

2. 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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# sum of two independent variables

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