FRM Fun 4. In the casino game of craps, the player rolls two six-sided dice. If the first roll is a 7 or 11, the player wins; if the first roll is a 2 or 12, the player loses. Normally, of course, the dice are independent and the expected outcome (mean) of rolling both dice is a seven (7). However, a crooked casino inserts magnets into the dice! With the hidden magnets, although each individual die remains a uniform distribution (i.e., probability = 1/6), the two dice are no longer independent but now have a positive correlation of + 0.50. The casino does this to make a roll of 2 (double ones) or 12 (double sixes) more likely. Questions: Does the expected sum of the two dice change, and if so, to what? Does the variance of the sum of the two dice change, and if so, to what?