Definition: Moment-generating function
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Moment-generating function
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Metadata: ID: D2 | shortcut: mgf | author: JoramSoch | date: 2020-01-22, 10:58.
Definition:
1) The moment-generating function of a random variable $X \in \mathbb{R}$ is
\[\label{eq:mgf-var} M_X(t) = \mathrm{E} \left[ e^{tX} \right], \quad t \in \mathbb{R} \; .\]2) The moment-generating function of a random vector $X \in \mathbb{R}^n$ is
\[\label{eq:mgf-vec} M_X(t) = \mathrm{E} \left[ e^{t^\mathrm{T}X} \right], \quad t \in \mathbb{R}^n \; .\]- Wikipedia (2020): "Moment-generating function"; in: Wikipedia, the free encyclopedia, retrieved on 2020-01-22; URL: https://en.wikipedia.org/wiki/Moment-generating_function#Definition.
- Taboga, Marco (2017): "Joint moment generating function"; in: Lectures on probability and mathematical statistics, retrieved on 2021-10-07; URL: https://www.statlect.com/fundamentals-of-probability/joint-moment-generating-function.
Metadata: ID: D2 | shortcut: mgf | author: JoramSoch | date: 2020-01-22, 10:58.