Difference between revisions of "Moment generating function"
From timescalewiki
(Created page with "Let $\mathbb{T}$ be a time scale with $0 \in \mathbb{T}$ and $\sup \mathbb{T}=\infty$. Let $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be a probability density function. ...") |
(No difference)
|
Revision as of 17:17, 23 November 2014
Let $\mathbb{T}$ be a time scale with $0 \in \mathbb{T}$ and $\sup \mathbb{T}=\infty$. Let $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be a probability density function. The moment generating function of $f$ is defined to be $$M_f(z) = \displaystyle\int_0^{\infty} f(t) e_z(t,0) \Delta t.$$
