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PROBLEM #2 Suppose you play a game in which a fair 6 sided die is rolled...

PROBLEM #2

Suppose you play a game in which a fair 6 sided die is rolled once. If the outcome of the roll (the number of dots on the side facing upward) is less than or equal to 4, you are paid as many dollars as the number you have rolled. Otherwise, you lose as many dollars as the number you have rolled.

Let X be the profit from the game (or the amount of money won or lost per roll). Negative profit corresponds to lost money.

  1. Fill out the following probability distribution table:

Roll Outcome

(X) Profit

Probability

XP(X)

  1. Compute the mean of X, (the expected profit)
  1. Explain the meaning of the expected value of X in the context of this problem.

  1. If you played this game 100 times, how much would you expect to win or lose?

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