Homework2

Statistics for Economist

100 points

  1. Investor has two stocks: stock A and stock B. Each stock may increase in value, decrease in value, or remain unchanged. Consider the experiment of investing in the tow stocks and observing the change (if any).
  2. How many experimental outcomes are possible?
  3. Show a tree diagram for the experiment
  4. How may of the experimental outcomes results in an increase in value for at least one of the tow stocks?
  5. How many of the experimental outcomes result in an increase in value for both of the stocks?
  6. An investor is reviewing the performance of six stocks and will select tow for investment. How many alternative combinations of two stocks does the investor have to consider?
  7. A pharmaceutical company conducted a study to evaluate the effectiveness of an allergy relief medicine; 250 patients with symptoms that included itchy eyes and a skin rash were given the new drug. The results of the study were as follows: 90 of the patients treated experienced eye relief, 135 had their skin rash clear up, and 45 experienced both relief from itchy eyes and the skin rash. What is the probability that a patient who takes the drug will experience relief for at least one of the two symptoms?
  8. A survey of the subscribers to Fortune magazine showed that 46% have mutual funds, 63% have money market funds, and 74% have mutual funds and/or money market funds (Fortune Subscriber Portrait, 1988). What is the probability a subscriber will not have investments in either type of fund?
  9. The Grant Thornton public accounting firm conducted a survey to see how executives felt about the 1992 recession and recovery potential (Journal of Accountancy, February, 1992). Results showed that the probability of an executive indicating the existence of a recession was .74. The probability of an executive stating that both a recession existed and recovery would occur within 6 month was .41.
  10. Given that an executive indicated the existence of a recession, what is the probability that the executive felt that a recovery would occur within 6 months?
  11. Assume that is an executive denied the existence of a recession, he or she also believed that a recovery had already begun. Construct a joint probability table for “recession,” “ no recession,” and “recovery,” “no recovery.” Those that feel a recovery is already underway and those who feel one will occur in 6 months should be put in the same category for this table.
  12. Use the joint probability table in (b) or find the marginal probability of a recovery.
  13. Find P(A), P(B), P(A|B), P(AB) and P(AB), Are A and B independent?
  1. A local bank is reviewing its credit-card policy with a view toward recalling some of its credit cards. In the pat approximately 5% of card holders have defaulted, and the bank has been unable to collect the outstanding balance. Thus management has established a prior probability of .05 that any particular cardholder will default. The bank has further found that the probability of missing one or more monthly payments for those customers who do not default is .20. Of course the probability of missing one or more payments for those who default is 1.
  2. Given that a customer has missed a monthly payment, compute the posterior probability that the customer will default.
  3. The bank would like to recall its card id the probability that a customer will default is greater than 0.20. Should the bank recall its card if the customer misses a monthly payment? Why or why not?

1. Do it by hand

2. Cheating or copying the homework will be penalized

3. Late handing in homework subject to 10 points deduction