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Exercise 2: Let X,Y and Z be random variables such that Cov(X, Y) < +oo. Show that Cov(X +E(X),Y + E(Y)) = E(Cov(X,Y||2) + Cov (E (X ||Z),E (Y||Z)).

Exercise 2: Let X,Y and Z be random variables such that Cov(X, Y) < +oo. Show that Cov(X +E(X),Y + E(Y)) = E(Cov(X,Y||2) + Cov (E (X ||Z),E (Y||Z)).

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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Exercise 2: Let X,Y and Z be random variables such that Cov(X,Y) < +0o. Show that Cov(X +E(X),Y +E(Y)) = E(Cov(X,Y |Z)) + Cov (E (X|||Z),E (Y||Z)).
Transcribed Image Text:Exercise 2: Let X,Y and Z be random variables such that Cov(X,Y) < +0o. Show that Cov(X +E(X),Y +E(Y)) = E(Cov(X,Y |Z)) + Cov (E (X|||Z),E (Y||Z)).
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