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Unformatted text preview: Answer Key for Final Practice Problems 1. Suppose that annual stock market returns are normally distributed with mean 6% and variance 16%. (a) If you invest in stocks, what is the probability that you will see a positive annual return? Let X be stock returns. Note: this problem could have been interpreted as X N (6 , 16) or X N (0 . 06 , . 16) (this would lead to different answers, both accepted for full credit). Here we use the first interpretation: P ( X 0) = P X- 6 16 - 6 4 = P ( Z - 1 . 5) = 1- P ( Z 1 . 5) = 0 . 933 (b) Alternatively, you can put the money in the bank and obtain a 4% return for sure (with prob- ability 1). What is the probability that you obtain a higher return by investing in stocks than by putting the money in the bank? For X stock returns, now we are looking for: P ( X 4) = P X- 6 16 4- 6 4 = P ( Z - . 5) = 1- P ( Z - . 5) = 0 . 691 (c) Historically, there have been a number of important stock market crashes, but no stock market booms of the same magnitude. What does this mean about the skewness of the distribution? Does this agree with the assumption that stock returns are normally distributed? The distribution of stock returns in skewed. Since the normal distribution is symmetric, nor- mality is not a good assumption. 2. A political candidate hires you to find what is the level of support in the population. You poll a number of people and record their answers. Let X i = 1 if person i said they supported the candidate and X i = 0 otherwise. You are interested in building a confidence interval for= 0 otherwise....
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