Question suppose that x and y have correlation coefficient rho=.2 What is the value of the correlation coefficient between a) 1+2x and 3+4y b) 1+2x and 3-4y c) 1-2x and 3-4y Thank you!!!!!! Solution a) Corrl( 1+2x , 3+4y ) =E (1+2x -E(1+2x ) )( 3+4y-E(3+4y) )/ sqrt(V(1+2x)*V(3+4y)) =E(2x-2E(x))(4y-4E(y))/sqrt(4V(x)*16V(y)) =2*4*E(x-E(x))(y-E(y))/2*4*sqrt(V(x)*V(y)) =E(x-E(x))(y-E(y))/sqrt(V(x)*V(y)) = Corr(x,y) =0.2 b) Corrl( 1+2x , 3-4y ) =E (1+2x -E(1+2x ) )( 3-4y-E(3-4y) )/ sqrt(V(1+2x)*V(3-4y)) =E(2x-2E(x))(-4y+4E(y))/sqrt(4V(x)*16V(y)) =2*-4*E(x-E(x))(y-E(y))/2*4*sqrt(V(x)*V(y)) =-E(x-E(x))(y-E(y))/sqrt(V(x)*V(y)) = -Corr(x,y) = -0.2 c) Corrl( 1-2x , 3-4y ) =E (1-2x -E(1-2x ) )( 3-4y-E(3-4y) )/ sqrt(V(1-2x)*V(3-4y)) =E(-2x+2E(x))(-4y+4E(y))/sqrt(4V(x)*16V(y)) =-2*-4*E(x-E(x))(y-E(y))/2*4*sqrt(V(x)*V(y)) =E(x-E(x))(y-E(y))/sqrt(V(x)*V(y)) = Corr(x,y) = 0.2.