Here are some sample test questions for Chapters 7 and 8. On an actual test, I will not put anything in parentheses about the topic. You are supposed to figure that out. Make sure that you write down an interpretation of the problem before you get to an equation.

A venture capitalist invests in companies. Each company either succeeds or fails. The probability of success is 10 percent. If a company fails, the venture capitalist loses $5 million on that investment. If the company succeeds, the venture capitalist gains $100 million.

1. (Expected Value) What is the expected value of an investment in one company?
2. (binomial distribution, pdf) Suppose that the venture capitalist invests in a portfolio of 12 companies. What is the probability that exactly 2 of the companies succeed?
3. (binominal distribution, cdf) With a portfolio of 12 companies, what is the probability that the number of companies that succeed is between 2 and 4 (that is, greater than 1 and less than 5)?
4. (binomial distribution mean and standard deviation) With a portfolio of 12 companies, what is the mean number of successes? What is the variance? What is the standard deviation?
5. (geometric distribution) What is the expected number of companies in which the venture capitalist will have to invest in order to achieve one success? What is the probability that the first twelve companies will fail and the thirteenth company will succeed?