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Given two independent random variables $X_1\in NB(p,r_1)$ and $X_2\in NB(p,r_2)$, find the distribution of random variable $X_1+X_2$

I came up with an answer that is obviously wrong since it's different from what's on the textbook ( $X_1+X_2 \in NB(p,r+s)$), how do I go about showing this?

ViC
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  • For future reference, you should include your work so that other can point out your mistakes or fix them. Also, make sure the parameters follow the same order. – Em. Mar 28 '17 at 04:17
  • I have fixed the parameters, thanks for the help! I'll keep that in mind for future reference. – ViC Mar 28 '17 at 04:26

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