81. Suppose a randomly chosen individual s verbal score X and quantitative score Y on a nationally administered aptitude examination have joint pdf You are asked to provide a prediction t of the individual s total score X  Y. The error of prediction is the mean squared error E[(X  Y  t)2]. What value of t minimizes the error of prediction?

f 1x, y2  •

2 5

12x  3y2 0 x

1, 0 y

1 0 otherwise f 1x, y2  e kxy x  0, y  0, 20 x  y 30 0 otherwise