I have a random variable $X$ defined by the sum of $k$ independent geometric distributions ($Y$) with parameter $p$, which makes it a negative binomial random variable $NB(k,p)$. The probability mass function of the geometric distribution is given by \begin{equation} \mathbb{P}(Y=y)=(1-p)p^{y} \end{equation} which is a different probability mass function than I have seen before. I can therefore not figure out what the probability mass function is of my random variable $X$. Does anyone know how I should approach this?
2026-02-24 04:33:07.1771907587
Probability mass function of alternative Negative binomial distribution
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