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What is the probability that i get at least my money

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There are 5 companies, each sells a bond that will pay $40 in one month. For each company the bond costs $30. All of these companies have probability 01 of default, and whether 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? What is 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 I cost? 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 mean and 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?

Reference no: EM132848938

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