There are 5 companies, each sells a bond that will pay $20 in one month. For eachcompany the bond costs $10. All of these companies have probability .01 of default, andwhether one defaults is independent from whether any of the others default.a) Let X be the number of companies that default. What is the distribution of X? Whatis the expected value of X? What is the variance of X?b) Consider two portfolios. In portfolio I, we buy one bond from each of these companies.In portfolio II, we buy 5 bonds from one of these companies. How much does portfolio Icost? How much does portfolio II cost?c) Let Y be the amount of money that we get in one month if we have portfolio I, and let Z be the amount of money that we get in one month if we have portfolio II. Find the meaand variance of Y and Z. Which has a higher mean and which has a higher variance?d) What is the probability that I get at least my money back from portfolio I.e) What is the probability that I get at least my money back from portfolio II.f) Which portfolio would you choose to buy? Why?

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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