## Math 160: Study Guide - Final Exam

1. Find the future value.
2. List the requirements for a linear programming problem to be in standard form.
3. Solve a 3x3 system of linear equations using Gauss-Jordan elimination. You may use the pivot program on the calculator.
4. Find the payment of a present value problem.
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.
6. Solve the matrix equation for X. Two parts.
7. Take a tableau from a Dual problem and identify the values of the variables for the dual and primal problems.
8. Given P(A), P(B) and one more probability, complete a probability distribution and then find several probabilities from the probability distribution.
9. Solve a game matrix, giving the optimal row and column strategies, and the value of the game.
10. Leontief input output problem.
11. Maximize or minimize a non-standard linear programming problem.
12. Markov chain problem. Write the initial state matrix, the transition matrix. Find the first state matrix, and the steady state matrix.
13. Decision Theory. Create the payoff table and the opportunistic loss table. Then give the value and optimal action under each criteria.
14. 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.
15. 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.
16. Retirement problem. Figure out what the need to retire and what it will take each month to save that.
17. Modified poker hand. Find five poker probabilities when certain cards are thrown out.
18. Find the mean, median, and sample standard deviation for a set of data.
19. Complete a truth table.

### 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.