suppose you play a game in which a fair if 6 sided die is rolled once. if the ne

Question

suppose you play a game in which a fair if 6 sided die is rolled once. if the

neay Stat have roles a e rol Let & te the araft from the gane jt the anoune of nasey won or lout i a roi Negative grofn a whhat ts your profit, X t the outcome of the roll is 5 it poim b. Fit oue the ylowing probability datributios table x) Guscame e Compute the moan of X, the expected profe 3 painta) d. Explsin the easing of the expected value of x in the contest of this problem. (2 poimts) e. If you played this game 100 times, how much would you expect to win or lose? (3 poims Show your work. Partial credit wil be geen

Explanation / Answer

(a) Here profit when the outcome is five is equals to - $5

(b) HEre the table is

(c) Mean

E[X] = 1 * 1/6 + 2 * 1/6 + 3 * 1/6 + 4 * 1/6 - 5 * 1/6 - 6 * 1/6 = -1/6

(d) Here expected value means that if we repeated play this game very large number of times, it would give us a profit of -$ 1/6 on average per game.

(E) Here if we played this game 100 times, we are likely to lose - $ 16.666

Roll 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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