In a game a player rolls a fair six-sided die. If the score is even, the player receives an amount of dollars equal to the score. If the score is odd, the player receives an amount of dollars equal to the score multiplied by three. It costs the player $5 to play the game.
(a) What is the probability mass function of the player's net winnings?
(b) What are the expectation and the standard deviation of the net winnings?
(c) Suppose that a player plays the game 10 times. What are the expectation and the standard deviation of the total net winnings from all 10 games?