st371-18 joint rv 02

st371-18 joint rv 02 - ST371 Introduction to Probability...

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(c) Tom Gerig ST371-18 joint rv 02 Page 1 ST371 Introduction to Probability and Distribution Theory Joint Probability Distributions Continuous Random Variables
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(c) Tom Gerig ST371-18 joint rv 02 Page 2 Outline Independence of two 's rv Continuous random variables: Joint of ( , ) Marginal distribution ( ) of Conditional distribution of given pdf X Y pdf X X Y y
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(c) Tom Gerig ST371-18 joint rv 02 Page 3 (( , ) ) ( , } P X Y A P a X b c Y d ( , ) bd ac f x y dydx  { , } A a X b c Y d Joint Distribution of Two Continuous Random Variables Let and be continuous random variables. Their joint probability density function ( ), ( , ) has the property that for XY jpdf f x y
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(c) Tom Gerig ST371-18 joint rv 02 Page 4 Joint Distribution of Two Continuous Random Variables The has the properties: jpdf ( , ) 1 f x y dydx      ( , ) 0 for all choices of and f x y x y , xy        
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(c) Tom Gerig ST371-18 joint rv 02 Page 5 2 2 2 0 0 0 0.25 0.25 2 0.5(2) 1 dydx dx   The joint for ' and is pdf rv s X Y 0.25, 0 2, 0 2 ( , ) 0, otherwise xy f x y Joint - Example I
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(c) Tom Gerig ST371-18 joint rv 02 Page 6 2 2 Support plane for ( , ): jpdf f x y 0 Joint - Example I pdf x y
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(c) Tom Gerig ST371-18 joint rv 02 Page 7 1 0.5 00 ( 1, 0.5) 0.25 P X Y dydx  11 0.5 0
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st371-18 joint rv 02 - ST371 Introduction to Probability...

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