2. Suppose you play a die rolling game in which a fair 6-sided die is rolled once. If the outcome of the roll (the number of dots on the side facing upward) is at least five, you win $9. If you roll a four, you pay $5. If you roll a three or less, you pay \$4. Let X be the profit of the game or the amount of money won or lost per roll. Negative profit corresponds to lost money. a) (6pt) Construct a probability distribution for the given information. b) (3pt) Compute the expected value (the mean) of X. c) (2pt) Explain the meaning of the expected value X in the context of the problem. d) (1pt) If you play this game 150 times, how much would you expect to win or lose