Solution Found!
Let Y1 and Y2 be uncorrelated random variables and
Chapter 5, Problem 94E(choose chapter or problem)
Problem 94E
Let Y1 and Y2 be uncorrelated random variables and consider U1 = Y1 + Y2 and U2 = Y1 − Y2.
a Find the Cov(U1, U2) in terms of the variances of Y1 and Y2.
b Find an expression for the coefficient of correlation between U1 and U2.
c Is it possible that Cov(U1, U2) = 0? When does this occur?
Questions & Answers
QUESTION:
Problem 94E
Let Y1 and Y2 be uncorrelated random variables and consider U1 = Y1 + Y2 and U2 = Y1 − Y2.
a Find the Cov(U1, U2) in terms of the variances of Y1 and Y2.
b Find an expression for the coefficient of correlation between U1 and U2.
c Is it possible that Cov(U1, U2) = 0? When does this occur?
ANSWER:
Solution
Step 1 of 3
a) We have to find the
Given that
Now
=
=
=
=
We know that
=
=
[ Note: since ]
=
=
=
Hence