In a certain city, three newspapers A, B, and C are published. Suppose that 60 percent of the families in the city subscribe to newspaper A, 40 percent of the families subscribe to newspaper B, and 30 percent subscribe to newspaper C. Suppose also that 20 percent of the families subscribe to both A and B, 10 percent subscribe to both A and C, 20 percent subscribe to both B and C, and 5 percent subscribe to all three newspapers A, B, and C. What percentage of the families in the city subscribe to at least one of the three newspapers?

Suppose that one can simulate as many i.i.d. Bernoulli random variarbles with parameter p as one wishes. Explain how to use these to approximate the mean of the geometric distribution with parameter p.

If X has the Cauchy distribution, the mean of X does not exist. What would you expect to happen if you simulated a large number of Cauchy random variables and computed their average?