9. Suppose that the Colts football team have already decided to try a play involving a medium pass up the middle (L_P). They know that their opponents, the Texans, have three possible defensive strategies (e.g., there are 3 States of Nature). One, occurring with a 0.25 chance, is that they will defend against the run, in which case the Colts will gain 16 yards. Another, occurring with a 0.5 chance, is that they will defend against the medium pass, in which case the Colts will gain zero yards. The other possibility, occurring with a 0.25 chance, is that they will defend against the long pass, in which case the Colts will gain an average of 8 yards. Assume the teams getlinear utility, U_C(yards) = y.

Question is

What is the expected gain (in yards) on the play for the Colts? What is the expectedutilityon the play for the Colts?