Let the correlation coefficient between X and Y be 0.6 . Random variables Z and W are defined as Z=X+5 and W = Y 3 . What is the correlation coefficient between Z and W ?

Step-by-step solution

Given, r_ x y =0.6 aligned & z = x +5 ; w= y 3 & ~b _ zx =1 b_ w y = 1 3 aligned aligned & b_ x y =b_ z x b_ w y =(1) ( 1 3 )= 1 3 & ~b _ z w ~b _ x y = 1 3 ~b _ z w = b _ x y 3 = 0.6 3 =0.2 aligned