Difference between revisions of "Expected value"
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Let $\mathbb{T}$ be a [[time scale]]. Let $X$ be a random variable with [[probability density function]] $f \colon \mathbb{T} \rightarrow \mathbb{R}$. The expected value of $X$ is given by | Let $\mathbb{T}$ be a [[time scale]]. Let $X$ be a random variable with [[probability density function]] $f \colon \mathbb{T} \rightarrow \mathbb{R}$. The expected value of $X$ is given by | ||
| − | $$ | + | $$\mathbb{E}_{\mathbb{T}}(X) = \dfrac{dC_f}{dz}(0),$$ |
where $C_f$ is the [[cumulant generating function]] of $f$. | where $C_f$ is the [[cumulant generating function]] of $f$. | ||
Revision as of 17:21, 23 November 2014
Let $\mathbb{T}$ be a time scale. Let $X$ be a random variable with probability density function $f \colon \mathbb{T} \rightarrow \mathbb{R}$. The expected value of $X$ is given by $$\mathbb{E}_{\mathbb{T}}(X) = \dfrac{dC_f}{dz}(0),$$ where $C_f$ is the cumulant generating function of $f$.
