Stat400Lec14(Ch4.2,5.3)_ans_part1

# Stat400Lec14(Ch4.2,5.3)_ans_part1 - STAT 400(Chapter 4.2...

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STAT 400 (Chapter 4.2) Spring 2012 4.2 Covariance and Correlation Coefficient Covariance of X and Y XY = Cov ( X , Y ) = E [ ( X – X ) ( Y – Y ) ] = E ( X Y ) X Y (a) Cov ( X , X ) = Var ( X ) ; (b) Cov ( X , Y ) = Cov ( Y , X ) ; (c) Cov ( a X + b , Y ) = a Cov ( X , Y ) ; (d) Cov ( X + Y , W ) = Cov ( X , W ) + Cov ( Y , W ) . Cov ( a X + b Y , c X + d Y ) = a c Var ( X ) + ( a d + b c ) Cov ( X , Y ) + b d Var ( Y ) . Var ( a X + b Y ) = Cov ( a X + b Y , a X + b Y ) = a 2 Var ( X ) + 2 a b Cov ( X , Y ) + b 2 Var ( Y ) . 0. Find in terms of X 2 , Y 2 , and XY : a) Cov ( 2 X + 3 Y , X – 2 Y ), Cov ( 2 X + 3 Y , X – 2 Y ) = 2 Var ( X ) – Cov ( X , Y ) – 6 Var ( Y ). b) Var ( 2 X + 3 Y ), Var ( 2 X + 3 Y ) = Cov ( 2 X + 3 Y , 2 X + 3 Y ) = 4 Var ( X ) + 12 Cov ( X , Y ) + 9 Var ( Y ). c) Var ( X – 2 Y ). Var ( X – 2 Y ) = Cov ( X – 2 Y , X – 2 Y ) = Var ( X ) – 4 Cov ( X , Y ) + 4 Var ( Y ).

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Correlation coefficient of X and Y
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Stat400Lec14(Ch4.2,5.3)_ans_part1 - STAT 400(Chapter 4.2...

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