Show that the negative binomial distribution is in the (a, b, 0)-class and determine the parameters a and b for a negative binomial distribution with mean 12 and variance 17.
Wich tools I have to use to solve this problem ?
2026-02-23 13:33:11.1771853591
Negative binomial distribution (a, b, 0)-class
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Well you have your explicit distribution, I think you can directly calculate $p_{k+1}/p_{k}$ so you can get $a$ and $b$.
From then you have a way friendlier expression for your distribution which would allow to get the mean and the variance depending from $a$ and $b$