seniorProbability
What is a probability generating function (PGF)?
Updated May 17, 2026
Short answer
A PGF encodes a discrete random variable’s distribution into a power series.
Deep explanation
The probability generating function G(s)=E[s^X] represents a discrete distribution compactly. It is useful for computing moments, analyzing branching processes, and solving recurrence relations in stochastic systems.
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