10 solution a the correlation between x and y is de

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Unformatted text preview: nd then derive the correlation coe cient = covX; Y = X Y  between X and Y . 10 Solution: a The correlation between X and Y is de ned as E X Y : 2 E X Y = E X aX + b = aE X 2 + bmX = a X + m2  + bmX X b First, we nd the mean of Y to be mY = E aX + b = amX + b. It follows then that the covariance between X and Y is 2 2 covX; Y  = E X Y , mX mY = a X + m2  + bmX , am2 , bmX = a X X X c We also know from class that Y = a X . Hence,  2 covX; Y  = a X = 1; a 0 = 2 ,1; a 0 jaj X XY 2 22 2 7 2 6 2 8 6. Suppose two r.v.'s X and...
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This note was uploaded on 03/10/2013 for the course ECE 3075 taught by Professor Staff during the Fall '08 term at Georgia Tech.

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