GE 331-Lecture 14

# GE 331-Lecture 14 - Lecture 14 IE 300/GE 331 Lecture 14...

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IE 300/GE 331 Lecture 14 Negar Kiyavash, UIUC 1 Lecture 14

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IE 300/GE 331 Lecture 14 Negar Kiyavash, UIUC 2 Quiz • Quiz: Let X be a uniform random variable on the interval [-2,4]. Let . Find E[Y]. X e Y
IE 300/GE 331 Lecture 14 Negar Kiyavash, UIUC 3 Two discrete r.v.’s Example: Check airline schedules using cell phones: 1 2 3 4 0.15 0.10 0.05 0.30 3 0.02 0.10 0.05 0.17 2 0.02 0.03 0.20 0.25 1 0.01 0.02 0.25 0.28 0.20 0.25 0.55 Y: # of times cite name is stated X: # of bars of signal strength

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IE 300/GE 331 Lecture 14 Negar Kiyavash, UIUC 4 Two discrete r.v.’s • Joint probability mass function of X,Y : f XY (1,2)=P(X=1,Y=2)=0.02, etc. • Requirements: 1 ) , ( 0 1 ) , ( , y x f y x f XY y x XY ) , ( ) , ( y Y x X P y x f XY
IE 300/GE 331 Lecture 14 Negar Kiyavash, UIUC 5 Marginal probability distribution Marginal probability mass function of X Condition probability mass funciton of Y given X=x y XY X y x f x X P x f ) , ( ) ( ) ( ) ( / ) , ( ) ( / ) , ( ) | ( ) ( | x f y x f x X P x X y Y P x X y Y P y f X XY x Y

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IE 300/GE 331 Lecture 14 Negar Kiyavash, UIUC 6 Conditional probability distribution • The condition probability mass funciton of Y given X=x P(Y=4|X=1)=f
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GE 331-Lecture 14 - Lecture 14 IE 300/GE 331 Lecture 14...

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