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Probability-Generating Function: Discrete Random Variable, Power Series, Generating Function -

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2026-04-08
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory, the probability-generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability-generating functions are often employed for their succinct descri ... Täydellinen kuvaus

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Kuvaus

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory, the probability-generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability-generating functions are often employed for their succinct description of the sequence of probabilities Pr(X = i) in the probability mass function for a random variable X, and to make available the well-developed theory of power series with non-negative coefficients. Probability-generating functions obey all the rules of power series with non-negative coefficients. In particular, G(1¿) = 1, where G(1¿) = limz¿1G(z) from below, since the probabilities must sum to one. So the radius of convergence of any probability-generating function must be at least 1, by Abel''s theorem for power series with non-negative coefficients.

Lisätietoja

Julkaisija OmniScriptum
Julkaisuvuosi 2026
Kannen tyyppi Pehmeäkantinen
EAN 9786133671171
Kirjoita oma arvostelusi
Arvostelet: Probability-Generating Function: Discrete Random Variable, Power Series, Generating Function
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168,40 € 224,53 €