## Math 160: Chapter 6 Study Guide

1. You are given a joint frequency distribution and asked to identify the number in an event.
2. You are given portions of a joint probability distribution and enough information to complete the table. Complete the table, and then find some probabilities. Be able to tell if two events are independent. Look at 6.5.1 - 6.5.16.
3. Decision Analysis problem. A payoff table is given. Compute the opportunistic loss table. Find the payoff or loss under the expected value, maximax, maximin, and minimax criterions.
4. Define the terms given. Know the definitions of Mutually exclusive events, independent events, equally likely events, all inclusive events, and fair game.
5. Find the probability of poker hands. The problem has been modified by removing some of the cards from the deck, so be careful. Look at problems 6.3.51 - 6.3.58. Show the setup and find the answer. You may use the hypergeometric program to find the probabilities for you.
6. A bag contains different types of bills. Find the probability of a randomly selected bill being of a particular kind. Find the probability of the second bill being of a particular kind if you 1) replace the first, 2) don't replace the first and know what it was, and 3) don't replace the first, but don't know what it was.
7. Finish a series of a game. Create a tree diagram, find the probability that each team wins. Look at problem 6.5.40.
8. Bayesian problem. Create a joint probability distribution from the information given. Then find some probabilities. Some of the probabilities are marginals, some are joint, some are conditional. You need to be able to figure out which is which by reading the problem. Look at problem 6.6.39 - 6.6.47.

### Notes:

• Problems 1 - 4 must be worked individually.
• Problems 4 - 8 may be worked in groups of up to 3 people.
• Because problems 1 - 4 took the instructor 6.5 minutes to take, and problems 5 - 8 took the instructor 13 minutes to take, there is no way the instructor envisions people getting through the entire test in 50 minutes _IF_ you don't split the work on the group part.
• Since the instructor knows you're not going to do this even though he recommends it strongly, the test will be given in two parts.
• Friday, March 7th, will be group.
• Tuesday, March 11, will be individual portion.
 # 1 2 3 4 5 6 7 8 Total Points 9 18 19 6 12 12 12 12 100