Suppose a game is played by rolling two six-sided dice and subtracting the smaller number from the larger number rolled. So, for instance, if you roll a 3 and a 5, the resulting score is 5 - 3 = 2. If both dice show the same number, take the score to be 0. Let the random variable X be your score on one roll of the dice.
(a) What is the probability distribution function for X?
(b) What is E(X)?
(c) What is Var(X)?