Difference between revisions of "Expected value"
From timescalewiki
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$$\mathbb{E}_{\mathbb{T}}(X) = \dfrac{dC_f}{dz}(0),$$ | $$\mathbb{E}_{\mathbb{T}}(X) = \dfrac{dC_f}{dz}(0),$$ | ||
where $C_f$ is the [[cumulant generating function]] of $f$. | where $C_f$ is the [[cumulant generating function]] of $f$. | ||
| + | |||
| + | =References= | ||
| + | [https://mospace.umsystem.edu/xmlui/bitstream/handle/10355/29595/Matthews_2011.pdf?sequence=1 Probability theory on time scales and applications to finance and inequalities by Thomas Matthews] | ||
Revision as of 17:26, 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 $f$.
References
Probability theory on time scales and applications to finance and inequalities by Thomas Matthews
