Expected value of random variables - On average, how many points do you expect to receive in each round of this game?
Suppose you have 2 fair dice, one is red and the other is blue, and both have numbers 1 through 6 on their faces. You play a game in which you toss both dice, then the number of points you win is given by raising the result of the blue die to the power 2 and multiplying it by 8; while the number of points you lose is given by raising the result of the red die to the power 2 and multiplying it by 9. On average, how many points do you expect to receive in each round of this game?
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