1. Cov(aX, Y) = aCov(X, Y). 2. Cov(X + Z,Y) = Cov(X, Y) + Cov(Z,Y). 3. Cov(aX+bZ,Y)= aCov(X,Y) +bCov(Z,Y).

Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter6: Circles
Section6.CT: Test
Problem 11CT: aIf HP=4, PJ=5, and PM=2, find LP. _ bIf HP=x+1, PJ=x1, LP=8, and PM=3, find x. _
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For any continuous random variables X, Y , Z and any constants a, b, show the following from the definition of the covariance:

 

1. Cov(aX,Y)=aCov(X, Y).
2. Cov(X + Z,Y)= Cov(X, Y) + Cov(Z,Y).
3. Cov(aX+bZ,Y)= aCov(X, Y) +bCov(Z,Y).
Transcribed Image Text:1. Cov(aX,Y)=aCov(X, Y). 2. Cov(X + Z,Y)= Cov(X, Y) + Cov(Z,Y). 3. Cov(aX+bZ,Y)= aCov(X, Y) +bCov(Z,Y).
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