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Var(X) = 8, Var(Y) = 4, Cov(X, Y) = -2. d the values of the following quantities. Please show your work. Cοv(Υ, X) nt: by using the definition Cov(X, Y) = E[(X – EX)(Y – EY)], observe that (X, Y) = Cov(Y, X).] %3D Cov(X, X) nt: by using the definition of covariance and variance, observe that (Х, X) %3DVar(X). ) Var(X + Y) nt: use the identity Var(X + Y) = Var(X)+ Var(Y)+2Cov(X, Y ).) Var(X + X) Cov(X, -X) nt: use the identity Cov(aX, bY) = ab · Cov(X, Y). )

Var(X) = 8, Var(Y) = 4, Cov(X, Y) = -2. d the values of the following quantities. Please show your work. Cοv(Υ, X) nt: by using the definition Cov(X, Y) = E[(X – EX)(Y – EY)], observe that (X, Y) = Cov(Y, X).] %3D Cov(X, X) nt: by using the definition of covariance and variance, observe that (Х, X) %3DVar(X). ) Var(X + Y) nt: use the identity Var(X + Y) = Var(X)+ Var(Y)+2Cov(X, Y ).) Var(X + X) Cov(X, -X) nt: use the identity Cov(aX, bY) = ab · Cov(X, 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 two random variables X and Y, we have Var(X) = 8, Var(Y) = 4, Cov(X, Y) = -2. Find the values of the following quantities. Please show your work. (a) Cov(Y, X) (Hint: by using the definition Cov(X, Y) = E[(X – EX)(Y – EY)], observe that Cov(X, Y) = Cov(Y, X). ] (b) Cov(X, X) (Hint: by using the definition of covariance and variance, observe that Cov(X, X) = Var(X). ) (c) Var(X + Y) (Hint: use the identity Var(X + Y) = (d) Var(X + X) Var(X)+ Var(Y) + 2Cov(X, Y). ) (e) Cov(X, -X) (Hint: use the identity Cov(aX, bY) = ab · Cov(X,Y). )
Transcribed Image Text:For two random variables X and Y, we have Var(X) = 8, Var(Y) = 4, Cov(X, Y) = -2. Find the values of the following quantities. Please show your work. (a) Cov(Y, X) (Hint: by using the definition Cov(X, Y) = E[(X – EX)(Y – EY)], observe that Cov(X, Y) = Cov(Y, X). ] (b) Cov(X, X) (Hint: by using the definition of covariance and variance, observe that Cov(X, X) = Var(X). ) (c) Var(X + Y) (Hint: use the identity Var(X + Y) = (d) Var(X + X) Var(X)+ Var(Y) + 2Cov(X, Y). ) (e) Cov(X, -X) (Hint: use the identity Cov(aX, bY) = ab · Cov(X,Y). )
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