Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [probability-generating-fn]

A probability generating function is a function defined as a power series which contain all the probability mass function values of a discrete probability distribution. It is related to the moment generating function, and also known as a z-transform.

Wikipedia has an article https://en.wikipedia.org/wiki/Probability-generating_function with further references.

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Probability Generating Functions: How to use them?

For a discrete variable $X$ that takes on nonnegative integer values $\{0,1,2,\ldots\}$, the probability generating function is defined as $$G(s) = \sum_{k=0}^\infty P(X=k) s^k$$ It is easy to show that the $n^{th}$ derivative at unity…
user1936752
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Probability generating function of mixture of discrete random variables

Consider a discrete distribution $X$ that is a mixture of two discrete distributions $A$ and $B$. Explicitly, $X=A$ with probability $p$ and $X=B$ with probability $1-p$. Denote the pgfs of $A$ and $B$ as $\mathcal{G}_A$ and $\mathcal{G}_B$…
Andrew
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Average cost of getting a specific card from deck of 9?

In a game, I am looking to draw the hero card out of 9 possible cards. The first card (full deck) costs 300 gems. All subsequent draws cost 600 gems. I can either keep drawing one card at a time till I hit the hero card or reset the game at any…
Dro
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