In a game, you roll two fair dice and observe the uppermost face on each of the die. Let X1 be the number on the first die and X2 be the number of the second die. Let Y = X1 - X2 denote your winnings in dollars.
a. Find the probability distribution for Y .
b. Find the expected value for Y .
c. Refer to (b). Based on this result, does this seem like a game you should play?
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