Answer the following questions, fully justifying your answers:

a) Consider IBMs stock. Assume that there probability that its price will decrease next year. The rational expectation for the value of this probability is 60% and the corresponding 90% confidence interval is (40%,70%). Additionally, consider an investor who doesnt know probability and suffers from the over-precision bias. This investor is asked to provide an estimate for probability as well as a 90% confidence interval for it. What are plausible values for these?

b) What is the belief in the law of small numbers? What are two fallacies related to the belief in the law of small numbers? What asset pricing anomalies can these explain? Discuss in detail.