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Practice set (Discrete Probability Distribution)P1.Returns on investments overseas, especially in Europe and the Pacific Rim, are expectedto be higher than those of U.S. markets in the near term, and analysts are now recommendinginvestments in international portfolios.An investment consultant believes that the probabilitydistribution of returns (in percent per year) on one such portfolio is as follows:x(%)P(x)90.05100.15110.30120.20130.15140.10150.05(a) Verify thatP(x) is a probability distribution.(b) What is the probability that returns will be at least 12%.(c) Find the cumulative distribution of returns.Solution:1