Negative Binomial Distribution Gives Rise to Probability Mass Function
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Theorem
Let $X$ be a discrete random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
First Form
Let $X$ have the negative binomial distribution (first form) with parameters $n$ and $p$ ($0 < p < 1$).
Then $X$ gives rise to a probability mass function.
Second Form
Let $X$ have the negative binomial distribution (second form) with parameters $n$ and $p$ ($0 < p < 1$).
Then $X$ gives rise to a probability mass function.