3. Law of Small Numbers Fund managers can be good, average, or bad with equal probability. Funds can increase, remain stable, or fall. If the fund manager is good, the fund increases with probability .8 and remains stable with probability .1. If the fund manager is average, the fund increases with probability .5 and remains stable with probability .3. If the manager is bad, the fund increases with probability .1 and remains stable with probability .4. Suppose the fund increases for two periods in a row and then falls. (a) What is the updated probability that the fund manager is good? [5 pts] (b) Suppose Jeff believes in the law of small numbers. If m=5 and N210, what is Jeff 's updated belief that the fund mananger is good? [10 pts] (c) Suppose Jeff believes in the law of small numbers. If m=5 and N=20, what is Jeff 's updated belief that the fund manager is good? [10 pts] (d) Explain the relationship between your ndings in (a), (b), and (c). [10 pts]