MomentGeneratingFunction

Available

Moment-generating function E[e^(tX)] of a probability distribution

Forms

MomentGeneratingFunction[dist, t]

MomentGeneratingFunction[dist, {t1, t2, …}]

Verified examplesMomentGeneratingFunction[PoissonDistribution[μ], t] → E^((-1 + E^t)*μ)MomentGeneratingFunction[NormalDistribution[μ, σ], t] → E^(μ*t + (σ^2*t^2)/2)MomentGeneratingFunction[NormalDistribution[], t] → E^(t^2/2)

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Topics

New In80 Alphabetical Listing - M
New In80 Mathematics And Algorithms - New Properties for Distributions »
Random Variables - Moments and Generating Functions »
Statistical Distribution Functions - Generating Functions »
Statistical Moments And Generating Functions - Moment-Generating Functions
Summation Transforms - Statistical Summation Transforms »

Related

Moment Expectation CharacteristicFunction CentralMomentGeneratingFunction FactorialMomentGeneratingFunction CumulantGeneratingFunction GeneratingFunction Cumulant HazardFunction LogLikelihood MarcumQ MathieuGroupM11

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