An investor considers investing $10,000 in the stock market. He believes that the probability is 0.30 that the economy will improve, 0.40 that it will stay the same, and 0.30 that it will deteriorate. Further, if the economy improves, he expects his investment to grow to $15,000, but it can also go down to $8,000 if the economy deteriorates. If the economy stays the same, his investment will stay at $10,000.
a. What is the expected value of his investment?
b. Should he invest the $10,000 in the stock market if he is risk neutral?
c. Is the decision clear-cut if he is risk averse? Explain.
At a local elementary school, a principal is making random class assignments for her 8 teachers. Each teacher must be assigned to exactly one job. In how many ways can the assignments be made?
Apparently, depression significantly increases the risk of developing dementia later in life (BBC News, July 6, 2010). In a study, it was reported that 22% of those who had depression went on to develop dementia, compared to only 17% of those who did not have depression. Suppose 10% of all people suffer from depression.
a. What is the probability of a person developing dementia?
b. If a person has developed dementia, what is the probability that the person suffered from depression earlier in life?