GE 331-Lecture 16

# GE 331-Lecture 16 - Announcements No Class on March 31st...

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IE 300/GE 331 Lecture 16 Negar Kiyavash, UIUC 1 Announcements: • No Class on March 31 st . • Second exam in less than a month: April 23 rd . • Ample time to study over the break.

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IE 300/GE 331 Lecture 16 Negar Kiyavash, UIUC 2 Quiz 4 The random variable X has the PDF: Let A be the event X>2, find conditional PDF of X given A. { ) ( 3 1 4 0 = x x else x f
IE 300/GE 331 Lecture 16 Negar Kiyavash, UIUC 3 Covariance • An statistical measure of how two random variable vary with respect to each other. Y μ X

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IE 300/GE 331 Lecture 16 Negar Kiyavash, UIUC 4 Covariance • Covariance measures linear relationship between two r.v.’s X and Y ) ( ) ( ) , cov( ) ( )] )( [( ) , cov( 2 2 X V X E X X XY E Y X E Y X X Y X Y X XY = = = = = μ σ
IE 300/GE 331 Lecture 16 Negar Kiyavash, UIUC 5 Covariance (cont) X μ Y ) )( ( Y X Y X

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IE 300/GE 331 Lecture 16 Negar Kiyavash, UIUC 6 Correlation Correlation also measures linear relationship between r.v.’s X and Y : easier to interpret • Satisfies Y X XY XY Y V X V Y X Y X corr σ ρ = = = ) ( ) ( ) , cov( ) , ( 1 1 XY
IE 300/GE 331 Lecture 16 Negar Kiyavash, UIUC 7 Independence • If X and Y are independent E(XY)=E(X)E(Y) • If X and Y are independent, • Independence Î zero covariance. Not vice versa 0 ) ( ) ( ) ( ) , cov( = = Y E X E XY E Y X

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IE 300/GE 331 Lecture 16 Negar Kiyavash, UIUC 8 Linear functions of r.v.s
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GE 331-Lecture 16 - Announcements No Class on March 31st...

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