# L12_S10 - AMS 507 Fall Semester 2010 Chapter Six Jointly...

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AMS 507, Fall Semester, 2010 Chapter Six Jointly Distributed Random Variables 6.1. Joint Distribution Functions The joint cumulative probability distribution function of any two random variables X and Y is defined by . , }, , { ) , ( , < < - = b a b Y a X P b a F Y X The cumulative distribution function of X is related to the joint cumulative probability distribution function by ), , ( ) ( , = a F a F Y X X and the cumulative distribution function of Y is related to the joint cumulative probability distribution function by ). , ( ) ( , b F b F Y X Y = In this context, ) ( a F X and ) ( b F Y are referred to as the marginal distribution functions of X and Y respectively. The probability of a rectangular region is given by ). , ( ) , ( ) , ( ) , ( } , { 1 1 1 2 , 2 1 , 2 2 , 2 1 2 1 b a F b a F b a F b a F b Y b a X a P Y X Y X Y X + - - = < < Definition of joint probability mass function of two discrete random variables: p x y P X x Y y ( , ) ( , ) . = = = One can calculate the marginal cumulative probability function of X as well as the marginal cumulative probability function of

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## This note was uploaded on 04/13/2010 for the course AMS 311 taught by Professor Tucker,a during the Spring '08 term at SUNY Stony Brook.

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L12_S10 - AMS 507 Fall Semester 2010 Chapter Six Jointly...

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