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Much is made of the fact that certain mutual funds outperform the market year after year (that is, the return from holding shares in the mutual fund is higher than the return from holding a portfolio such as the S&P 500). For concreteness, consider a 10-year period and let the population be the 4,170 mutual funds reported in The Wall Street Journal on January 1, 1995. By saying that performance relative to the market is random, we mean that each fund has a 50-50 chance of outperforming the market in any year and that perfor- mance is independent from year to year.
(i) If performance relative to the market is truly random, what is the probability that any particular fund outperforms the market in all 10 years?
(ii) Find the probability that at least one fund out of 4,170 funds outperforms the market in all 10 years. What do you make of your answer?
(iii) If you have a statistical package that computes binomial probabilities, find the probability that at least five funds outperform the market in all 10 years.
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If you like a challenge, consider what would happen if travel costs were linear instead of quadratic. If you do this, be prepared for enormous frustrations.
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A baseball player hits a home run. The height, in feet, of the ball t second after it is hit is given by h = -15t 2 + 96t + 4 - How high does the ball goes before returning to the ground?
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Suppose that she invests in a college education, expecting to get a better and higher wage job. Show how her optimal stock of health capital changes by the age of 30 due to the increased wage.
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