4.7 A box contains three balls, numbered 1, 2, 3. Ann randomly chooses a ball and writes down its number (without returning the ball to the box). Call the number X1. Then Bob randomly chooses a ball and writes down its number, which we’ll call Y1. The drawn balls are returned to the box. This procedure is done over and over, for a total of 1000 times, generating random variables X1, X2,...,X1,000 and Y1, Y2,...,Y1,000.

Let S =

1

,000 1

Xi and T =

1

,000 1

Yi be Ann’s and Bob’s respective totals. Find the correlation between S and T.