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# CH3 - Stat1301B Probability Statistics I Fall 2009-2010...

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Stat1301B Probability& Statistics I Fall 2009-2010 P.104 Chapter III Jointly Distributed Random Variables § 3.1 Joint and Marginal Distributions When an experiment or survey is conducted, two or more random variables are often observed simultaneously not only to study their individual probabilistic behaviours but also to determine the degree of relationship among the variables as in most of cases, the variables are related. The probabilistic behaviours of the random variables are described by their joint distribution . In the simplest case, suppose there are only two discrete random variables ( X , Y ) which take distinct values : Values of X : ( ) } ,..., , { 2 1 r x x x X = Ω Values of Y : ( ) } ,..., , { 2 1 c y y y Y = Ω Definition The joint probability mass function ( joint pmf ) of the discrete random variables X and Y and is defined by ( ) ( ) y Y x X P y x p = = = , , , ( ) Ω X x , ( ) Ω Y y . Sometimes the joint pmf can be conveniently presented in the form of a two-way table as Values of Y Values of X 1 y 2 y c y 1 x ( ) 1 1 , y x p ( ) 2 1 , y x p ( ) c y x p , 1 2 x ( ) 1 2 , y x p ( ) 2 2 , y x p ( ) c y x p , 2 r x ( ) 1 , y x p r ( ) 2 , y x p r ( ) c r y x p ,

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