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11. Let X and Y be two uncorrelated random variables with means μ and μy, and X variances of and o, respectively. If U = X + Y and V = X - Y, find the covariance and correlation coefficients of U and V, in terms of o' and o.

11. Let X and Y be two uncorrelated random variables with means μ and μy, and X variances of and o, respectively. If U = X + Y and V = X - Y, find the covariance and correlation coefficients of U and V, in terms of o' and o.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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11. Let X and Y be two uncorrelated random variables with means μx and μy, and variances of and o, respectively. If U = X + Y and V=X - Y, find the covariance and correlation coefficients of U and V, in terms of o' and o.
Transcribed Image Text:11. Let X and Y be two uncorrelated random variables with means μx and μy, and variances of and o, respectively. If U = X + Y and V=X - Y, find the covariance and correlation coefficients of U and V, in terms of o' and o.
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