# 22 each time the frozen yogurt machine at the mall

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Unformatted text preview: In the long run how often are jobs completed? 3.13. In the Duke versus Miami football game, possessions alternate between Duke who has the ball for an average of 2 minutes and Miami who has the ball for an average of 6 minutes. (a) In the long run what fraction of time does Duke have the ball? (b) Suppose that on each possession Duke scores a touchdown with probability 1/4 while Miami scores with probability one. On the average how many touchdowns will they score per hour? 3.14. Random Investment. An investor has \$100,000. If the current interest rate is i% (compounded continuously so that the grow per year is exp(i/100)), he invests his money in a i year CD, takes the proﬁts and then reinvests the \$100,000. Suppose that the k th investment leads to an interest rate Xk which is uniform on {1, 2, 3, 4, 5}. In the long run how much money does he make per year. 3.15. Consider the set-up of Example 3.4 but now suppose that the car’s lifetime h(t) = e t . Show that for any A and B the optimal time T = 1. C...
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