seniorProbability
What is a moment generating function (MGF)?
Updated May 17, 2026
Short answer
MGF uniquely characterizes a distribution using exponential expectations.
Deep explanation
The moment generating function M(t)=E[e^{tX}] encodes all moments of a distribution. Derivatives of M(t) at zero give moments like mean and variance. It is useful in proving limit theorems and identifying distributions.
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