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SIE 305 Test 2 Notesheet 2

# SIE 305 Test 2 Notesheet 2 - Chapter 5 Necessary Conditions...

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Chapter 5 Necessary Conditions for Discrete Joint Density - ∑∑ = x all y all 1 ) , ( 0 ) , ( y x f y x f XY XY Discrete Marginal Densities = = x all y all ) , ( ) ( ) , ( ) ( y x f y f y x f x f XY Y XY X Continuous Joint Density and Continuous Marginal Density (Change summations to integrals and set limits as – infinity to infinity). Independence [ ] [ ] [ ] ) ( ) ( ) , ( 2 1 2 1 y f x f y x f A P A P A A P Y X XY = = Expected Value [ ] [ ] [ ] - - - - - - = = = dydx y x yf Y E dydx y x xf X E dydx y x f y x H y x H E XY XY XY ) , ( ) , ( ) , ( ) , ( ) , ( Covariance [ ] [ ] [ ] [ ] [ ] [ ] [ ] 1 1 - ) )( ( ) , ( the t, independen are Y and X If ) )( ( ) , ( = = - = - - = XY XY Y X VarY VarX y x Cov Y E X E XY E Y E X E XY E y x E y x Cov ρ μ Conditional Density 0 ) ( ) ( ) , ( 0 ) ( ) ( ) , ( | | = = x f x f y x f f y f y f y x f f x x XY x Y y y XY y X Curve of regression Mean value of X given Y=y, denoted by M

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SIE 305 Test 2 Notesheet 2 - Chapter 5 Necessary Conditions...

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