2. Suppose you play a game in which a friend offers to play in which you roll a fair die. If the outcome of the die is a "1", he will give you $7 and if the outcome is "6", he will give you $4. But if the outcome is any other number, you owe him $3. Let X = Amount of money you gain in one round of this game (loss counted as negative). a. Fill out the probability distribution function below. Outcome "1" "6" "2", "3", "4" or "5" x ($) P(x): keep as fraction b. Find the expected value (mean) for X, the amount of money you gain in one round of this game, on average. Since it's measured in dollars, round your final answer to 2 decimal places. C. Find the amount of money your friend would gain in one round of this game, on average. Explain. d. How much money can you expect to win (or lose) if you play 20 rounds of this game with your friend?