EmplID: Part I (Form A) Elementary Statistics Departmental Final Exam (12 points

Question

EmplID: Part I (Form A) Elementary Statistics Departmental Final Exam (12 points) Problem # 3 Suppose you play a game in which a fair 6-sided die is rolled once. If the outcome of the roll ny (the number of dots on the side facing upward) is less than or equal to 4, you are paid as ma dollars as the number you have rolled. Otherwise, you loose 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 I a roll). Negative profit corresponds to lost money. a. What is your profit, X, if the outcome of the roll is 5? (1 point) b. Fill out the following probability distribution table: (5 points) Roll Outcome Probability Profit c. Compute the mean of X, (the expected profit). (3 points) d. Explain the meaning of the expected value of X in the context of this problem. (2 points) e. If you played this game 100 times, how much would you expect to win or lose? (1 points) Show your work. Partial credit will be given.

Explanation / Answer

(a) As 5 is greater than 4, for the outcome of the roll as 5, there will be a lose of 5 dollars.

Thus, the profit X = -5 dollars ( negative)

(b)

(X)

Profit

(c) The mean of X = 1/6*(1 + 2 + 3 + 4 - 5 - 6) = (-1/6)

Thus, expected profit is (-1/6 dollar) or an expected loss of 1/6 dollar.

(d) Expected value of X denotes the profit(or loss) [as per the sign of X] for one roll of a die.

(e) For 100 game, we would expect to lose (1/6)*100 = 16.67 dollars.

Roll outcome

(X)

Profit

Probability 1 1 1/6 2 2 1/6 3 3 1/6 4 4 1/6 5 -5 1/6 6 -6 1/6

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