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Unformatted text preview: aX + c,bY + d ) = sign ( ab ) Corr ( X,Y ) The sign and the magnitude of ρ reveal the direction and strength of the linear relationship between X and Y. Sum of independent random variables Let X 1 ,X 2 ,...,X n be independent random variables, Y = ∑ n i =1 a i X i , where a i s are constants. Then, E ( Y ) = ∑ n i =1 aE ( X i ) V ar ( Y ) = ∑ n i =1 V ar ( a i X i ) = ∑ n i =1 a 2 i V ar ( X i ) M y ( t ) = Q n i =1 M x i ( a i t ) 1 Problems Problem 1 Let X and Y be two discrete random variables with joint probability mass function shown in the table. (a)Calculate the covariance and correlation coecient between X and Y. (b)Determine whether X and Y are independent. 2 3...
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