briefnts4_randvt

briefnts4_randvt - Brief Notes #4 Random Vectors A set of 2...

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Brief Notes #4 Random Vectors A set of 2 or more random variables constitutes a random vector. For example, a random X 1 vector with two components, X = , is a function from the sample space of an X 2 experiment to the (x 1 , x 2 ) plane. Discrete Random Vectors Characterization Joint PMF of X 1 and X 2 : P X (x) = P X X , (x 1 x , ) = X [( P = x 1 ) (X = x 2 )] 2 1 2 1 2 Joint CDF of X 1 and X 2 : F X (x) = F X , X 2 ( x , x ) = X [( P x 1 ) (X x 2 )] 1 2 1 2 1 = ∑∑ P X , X ( u , u ) 1 2 u 1 x 1 u 2 x 2 1 2 Marginal Distribution Marginal PMF of X 1 : P X 1 (x ) = P[X = x 1 ] = X [( P = x 1 ) (X = x 2 )] = P X , X ( x , x ) 1 1 1 2 1 2 1 2 x all 2 x all 2 Marginal CDF of X 1 : F X 1 (x ) = P[X x 1 ] = X [( P x 1 ) (X < )] = F X , X ( , x = ∑∑ P X , X ( x , u ) 1 1 1 2 1 x all 2 u x 1 1 2 ) 1 2 2
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Continuous Random Vectors Characterization Joint CDF F X , X
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briefnts4_randvt - Brief Notes #4 Random Vectors A set of 2...

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