Consider a dice game: no points for rolling a 1, 2, or 3; 5 points for a 4 or 5; 50 points for a 6.
(a) Write the probability model for the points from this game, and find the expected value and the standard deviation.
(b) Imagine doubling the points awarded. What are the new mean and standard deviation?
(c) Now imagine just playing the game twice. What are the mean and the standard deviation of your total points from the two games?
(d) Suppose you and a friend both play the dice game. What are the mean and standard deviation of the difference in your points?