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Probability
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).

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).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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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