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Unformatted text preview: v(X, Y ), the standard deviation of 10X is 10σX , and the standard
deviation of Y + 4 is σ , ρ
= 10Cov(X,Y ) = Cov(X,Y ) = ρ
Y 10X,Y +4 (10σX )σY X,Y σX σY It is clear from the deﬁnition that the correlation coeﬃcient ρX,Y is a scaled version of Cov(X, Y ).
The units that E [XY ] or Cov(X, Y ) are measured in are the product of the units that X is measured in times the units that Y is measured in. For example, if X is in kilometers and Y is in
seconds, then Cov(X, Y ) is in kilometer-seconds. If we were to change units of the ﬁrst variable to
meters, then X in kilometers would be changed to 1000X in meters, and the covariance between
the new measurement in meters and Y would be Cov(1000X, Y ) = 1000Cov(X, Y ), which would be
measured in meter-seconds. In contrast, the correlation coeﬃcient ρX,Y is dimensionless–it carries
no units. That is because the units of the denominator, σX σY , in the deﬁnition of ρX,Y , are the
units of X times the units of Y, which are also t...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
- Spring '08
- The Land