Probability question

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Probability question

Postby vandana.jain » Tue Jul 24, 2012 5:00 pm

Hi Pristine,
Can u plz help me with this Question
If X & Y are two variables with same variance and U & V are two variables such that U = X + Y and V = X -Y. Then Covariance(U, V) is:
a. 1/2
b. 1
c. 0

Posts: 5
Joined: Mon Jul 30, 2012 2:59 pm

Re: Probability question

Postby searyv123 » Mon Jul 30, 2012 4:23 pm

Hi Vandana. Here is the Solution

Since Cov(X,Y) is bilinear you can "expand the brackets". Hence

Cov(X+Y,X-Y) = Cov(X,X) + Cov(Y,X) - Cov(X,Y) - Cov(Y, Y)

= Var(X) - Var(Y)

This is one of the Property of Covariance. few other Useful Properties of Covariance are

• Cov(X, X) = Var(X)
• Cov(X, Y) = Cov(Y, X)
• Cov(aX, bY) = abCov(X, Y) for constants a and b
• Cov(X+a, Y+b) = Cov(X, Y) for constants a and b

Hope this will help

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