Expected ValueObjectives:- Determine the expected value of an event.Vocabulary:- expected value- decision theoryPossible Classroom Examples:Of all workers at a certain factory, the proportions earning certain hourly wages are as follows:hourly wage$8.50$9.00$9.50$10.00$12.50$15.00proportion 20% 15% 25% 20% 15% 5%Find the expected hourly wage that a worker at this factory makes.Suppose you are taking a multiple-choice test where each questions has choices a through e. If you get the answer correct, you get 4 points. If you get a wrong answer, you lose 1 point.a. Find the expected value of a random guess.b. Find the expected value of eliminating one answer and guessing between the remaining 4 possible answers.c. Find the expected value of eliminating three answers and guessing between the remaining 2 possible answers.d. Use decision theory and your answers to parts a, b, and c to create a guessing strategy for this multiple-choice test.Expected Value Page 1 of 2Maria just inherited $10000. Her bank has a savings account that pays4.1% interest per year. Some of her friends recommended a new mutual fund, which has been in business for three years. During its first year, the fund went up in value by 10%; during the second year it went down by 19%; and during its third year, it went up by 145. Maria is attracted by the mutual fund’s potential for relatively high earnings but concerned by the possibility of actually losing some of her inheritance. The bank’s rate is low, but it is insured by the federal government. Use decision theory to find the best investment. (Assume that the fund’s past behavior predicts its future behavior.)Expected Value Page 2 of
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