A probabilistic experiment consists in rolling two un-biased dice, one painted red and

one painted blue. You roll the dice and you record the numbers showing on each die.

Let X be the random variable that records the number that you get by subtracting the

value on the red die from the value of the blue die.

(a) What is the probability distribution of X. (5 marks)

(b) You play a game with Burkard. You roll the dice and get X Freddo Frogs if X is

positive. If X is negative, you have to give Burkard −X Freddo frogs. Nothing

happens if X = 0. What are your expected winnings in terms of Freddo Frogs?

What is the standard deviation of this random variable? (5 marks)