Difference between revisions of "Joint time scales probability density function"
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# $f_{X,Y}(x,y) \geq 0$ for all $x,y \in \mathbb{T}$ | # $f_{X,Y}(x,y) \geq 0$ for all $x,y \in \mathbb{T}$ | ||
# $\displaystyle\int_0^{\infty} \int_0^{\infty} f_{X,Y}(x,y) \Delta y \Delta x=1$. | # $\displaystyle\int_0^{\infty} \int_0^{\infty} f_{X,Y}(x,y) \Delta y \Delta x=1$. | ||
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| + | =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] | ||
Latest revision as of 04:37, 6 March 2015
Let $\mathbb{T}$ be a time scale. Let $X$ and $Y$ be random variables. We say that $f_{X,Y}(x,y)$ is a joint time scales probability density function if
- $f_{X,Y}(x,y) \geq 0$ for all $x,y \in \mathbb{T}$
- $\displaystyle\int_0^{\infty} \int_0^{\infty} f_{X,Y}(x,y) \Delta y \Delta x=1$.
References
Probability theory on time scales and applications to finance and inequalities by Thomas Matthews
