An urn contains 7 black balls, 4 red balls, 3 white balls and 1blue ball, and a player is to draw one ball. If it is black, hewins $1, if it is red, he wins $2, if it is white he wins $3 and ifit is blue, he pay $25.
a. Set up the empirical probability distribution for the randomvariable X, the payoff of the game.
| Game Payoff (X) | Probability [P(X) |
| $1 | |
| $2 | |
| $3 | |
| $4 | |
b. What is the mathematical expectation of this game?
c. In the long-run, will the player win or lose?
