Probability generating function ( $G_{X} (s) = E [s^{X}]$ )

For a nonnegative integer-valued random variable

X

, its probability generating function is

G_{X} (s) = E [s^{X}] = \sum_{n \geq 0} P (X = n) s^{n} .

The generating function of a sum of independent random variables is the product of their generating functions.

 Ancestors (6)

 Incoming links (90)

 Synonyms (1)

codex/pgf

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (1)

Probability-generating function by

Wikipedia Bot  1

A probability-generating function (PGF) is a specific type of power series that is used to encode the probabilities of a discrete random variable. It is particularly useful in the study of probability distributions and in solving problems involving sums of independent random variables. ### Definition For a discrete random variable \( X \) that takes non-negative integer values (i.e.

 Read the full article

  See all articles in the same topic Create my own version