35. Let ZX be the standardized X, ZX(XmX)/sX, and let ZY be the standardized Y, ZY  (Y  mY)/sY.

a. Show with the help of the previous exercise that E[(ZY  rZX)]2  1  r2.

b. Use part

(a) to show that 1 r

1.

c. Use part

(a) to show that r  1 implies that Y 

aXb where a 0, and r1 implies that Y

aX  b where a  0.