Consider the following dice game, as played at a certain gambling casino: Players 1 and 2 roll a pair of dice in turn. The bank then rolls the dice to determine the outcome according to the following rule: Player i, i = 1, 2, wins if his roll is strictly greater than the bank€™s. For i = 1, 2, let

and show that I1 and I2 are positively correlated. Explain why this result was to be expected.

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1 ifíwins i=10 otherwise