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LEC18 Joint Dist

# LEC18 Joint Dist - Joint Distributions for Discrete R.V...

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Joint Distributions for Discrete R.V. Consider 2 Discrete r.v. 's r.v. X with possible values x = x 1 , x 2 , . .. r.v. Y with possible values y = y 1 , y 2 , . .. The joint distribution function is a list of outcomes of X and Y: (x 1 , y 1 ), (x 1 , y 2 ), (x 1 , y 3 ), (x 2 , y 1 ), (x 2 , y 2 ), . ... plus the probability associated with each outcome

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Example r.v. X = speed in feet per second; X=1,2, 3 r.v. Y = number of defects ; Y=1,2 defects Y=1 Y=2 speed X=1 .20 .10 X=2 .15 .40 X=3 .05 .10 Joint Distribution of X and Y: f P X Y f P X Y f f f f X Y X Y X Y X Y X Y X Y , , , , , , ( , ) ( ) . ( , ) ( ) . ( , ) . ( , ) . ( , ) . ( , ) . 1 1 1 1 20 1 2 1 2 10 2 1 15 1 2 40 3 1 05 1 2 10 = = = = = = = = = = = = 2
Marginal distribution defects Y=1 Y=2 speed X=1 .20 .10 X=2 .15 .40 X=3 .05 .10 Find marginal distribution of X. f P X f f X X X ( ) ( ) ( ) ( ) 1 1 2 3 = = = = = 3

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Conditional Distribution defects Y=1 Y=2 speed X=1 .20 .10 X=2 .15 .40 X=3 .05 .10 Find the conditional distribution of defects, Y, given speed, X, is 1 foot per second. r.v. Y = 1, 2
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LEC18 Joint Dist - Joint Distributions for Discrete R.V...

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