Suppose that you are offered the following "deal." You roll a die. If you roll a 6, you win $10. If you roll a 4 or 5, you win $5. If you roll a 1, 2, or 3, you pay $6. a. What are you ultimately interested in here (the value of the roll or the money you win)? b. In words, define the Random Variable X. c. List the values that X may take on. d. Construct a PDF. e. Over the long run of playing this game, what are your expected average winnings per game? f. Based on numerical values, should you take the deal? Explain your decision in complete sentences.