## Math 160: Study Guide - Final Exam

1. Find the future value. Use the "finance" program.
2. List the requirements for a linear programming problem to be in standard form.
3. Matrix multiplication problem. Find the product of two matrices, interpret the product by labeling the rows and columns. Look at the boat problem out of section 4.4.
4. Find the payment of a present value problem. Use the "finance" program.
5. Create a payoff table for a game. Then create a probability distribution and find the expected value. Identify whether the game is fair or not. You may use the "pdist" program, although it's probably easier to do by hand.
6. Solve the matrix equation for X. Two parts.
7. Solve a 3x3 system of linear equations. Either use Gauss-Jordan elimination (pivoting) or use the inverse of a matrix.
8. Find probabilities. Part of it can be done using the hypergeometric distribution, but you will also need to use the multiplication rule for independent events.
9. The initial tableau from a non-standard maximization problem is given. Write the maximization problem.
10. Given P(A), P(B) and one more probability, complete a probability distribution and then find several probabilities from the probability distribution.
11. Solve a game matrix, giving the optimal row and column strategies, and the value of the game. Use the "game" program.
12. Leontief input output problem. Use the "leontief" program.
13. Maximize a standard linear programming problem. Write the initial tableau and final tableau, and give the values of the objective function and decision variables. Use the "simplex" program.
14. Markov chain problem. Write the initial state matrix, the transition matrix. Find the first state matrix, and the steady state matrix.
15. Decision Theory. Create the payoff table and the opportunistic loss table. Then give the value and optimal action under each criteria.
16. Probability problem. Two bags with different types of coins in them. Draw a coin out of bag 1 and place it into bag 2 and then find some probabilities. Also randomly select a bag and draw a coin from it and find some probabilities.
17. Absorbing Markov chain problem. Write the initial state matrix and the transition matrix. Then find the expected number of transient states before leaving the matrix.
18. Retirement problem. Figure out what the need to retire and what it will take each month to save that. Use the "finance" program.
19. Modified poker hand. Find five poker probabilities when certain cards are thrown out. Use the "hypergeo" program.
20. Find the mean, median, and sample standard deviation for a set of data.
21. Binomial probabilities. Use the "binom" program.
22. The final tableau from a zero-sum, two-player game is given. Give the optimal row and column strategies and the value of the game.

### Notes:

• The test is open notebook. Make sure that your notes are complete in the sections covered on the exam.
• After approximately one hour, you will be able to get into groups of up to three people. However, when you get into groups, you lose your notebooks. For this reason, get as much of the information transferred from your notes onto your test as necessary before you get into groups.
• You do not have to get into groups when permission is granted. You may continue to work alone with your notes until you're ready to get into groups.
• There are more than 200 points possible on the exam, so don't be concerned if you can't work every problem.
 # 1 2 3 4 5 6 7 8 9 10 11 Pts 6 6 9 6 11 6 6 9 6 18 9 12 13 14 15 16 17 18 19 20 21 22 Total 6 7 12 16 21 9 10 15 12 9 9 218