# 27 the number showing for one roll of a die has mean

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: he units of the numerator, Cov(X, Y ). The situation is similar to the use of the standardized versions of random variables X and Y , namely X −E [X ] σX and Y −E [Y ] . These standardized versions have mean zero, variance one, and are dimensionless. In σY fact, the covariance between the standardized versions of X and Y is ρX,Y : Cov X − E [X ] Y − E [Y ] , σX σY = Cov XY , σX σY = Cov(X, Y ) = ρX,Y . σX σY If the units of X or Y are changed (by linear or aﬃne scaling, such as changing from kilometers to meters, or degrees C to degrees F) the correlation coeﬃcient does not change: ρaX +b,cY +d = ρX,Y for a, c > 0. In a sense, therefore, the correlation coeﬃcient ρX,Y is the standardized version of the covariance, Cov(X, Y ), or of the correlation, E [XY ]. As shown in the corollary of the following proposition, correlation coeﬃcients are always in the interval [−1, 1]. As shown in Section 4.10, covariance or correlation coeﬃcients play a central role for estimating Y by a linear...
View Full Document

## 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.

Ask a homework question - tutors are online