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Joint Distribution Function

المؤلف:  Grimmett, G. and Stirzaker, D

المصدر:  Probability and Random Processes, 2nd ed. New York: Oxford University Press, 1992

الجزء والصفحة:  ...

20-4-2021

1860

Joint Distribution Function

A joint distribution function is a distribution function  in two variables defined by

			(1)
			(2)
			(3)

so that the joint probability function satisfies

(4)

(5)

		{X in (-infty,x],Y in (-infty,y]}" src="https://mathworld.wolfram.com/images/equations/JointDistributionFunction/Inline13.gif" style="height:15px; width:172px" />	(6)
			(7)

(8)

Two random variables  and  are independent iff

(9)

for all  and  and

(10)

A multiple distribution function is of the form

(11)

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REFERENCES:

Grimmett, G. and Stirzaker, D. Probability and Random Processes, 2nd ed. New York: Oxford University Press, 1992.