## Math 160: Chapter 6/7 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. Statistics problem. Given a set of data, find the mean, median, range, and sample standard deviation.
6. Binomial problem. Use the calculator program to find two binomial probabilities. Also find the mean of the binomial distribution.
7. Normal probability. Look at problems 7.6.51, 53, 57, 61
8. 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 6.3.53 - 6.3.60. Show the setup and find the answer. You may use the hypergeometric program to find the probabilities for you.
9. 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.
10. Finish a series of a game. Create a tree diagram, find the probability that each team wins. Look at problem 6.5.42.
11. 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 6.6.41 - 6.6.49.

### Notes:

• Problems 1 - 7 must be worked individually.
• Problems 8 - 11 may be worked in groups of up to 4 people.
• You must turn in the first portion of the exam before getting into groups.
 # 1 2 3 4 5 6 7 8 9 10 11 Total Pts 6 17 10 6 8 6 4 9 12 10 12 100