# Math 160: Study Guide - Final Exam

1. Compound interest problem. Use the "finance" program.
2. Present value problem. Use the "finance" program.
3. Future value problem. Use the "finance" program.
4. Give the solution to a system of linear equations from an augmented matrix in reduced row echelon form.
5. Give the solution to a system of linear equations from an augmented matrix in row echelon form.
6. Solve a 3x3 system of linear equations. Either use Gauss-Jordan elimination (pivoting or the rref calculator command) or use the inverse of a matrix.
7. Solve the matrix equations for X. Three parts.
8. The initial system to a linear programming problem is given. Complete the table of values, determine if the points are feasible or not, and give the optimal solution to the problem.
9. The preliminary tableau from a non-standard maximization problem is given. Write the maximization problem. Do not solve the problem.
10. 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.
11. Linear programming problem. A tableau is given. Label the columns as appropriate using x's for the decision variables, s's for the slack variables, z for the objective function, and rhs for the right hand side. Identify which variables are basic and which are non-basic and give their values. Identify the basic variable for each row of the tableau and find the appropriate ratios on the right side. Circle the pivot element. Identify which variable is entering and which is exiting.
12. Use a venn diagram to find the number and or probability of events.
13. Find the number of ways an event can happen. Similar to the "how many three digit license places can be formed if ..." problems in chapter 6.
14. Bayesian probability problem. Complete the joint probability distribution and then use it to answer the questions.
15. Given P(A), P(B) and one more probability, complete a probability distribution and then find several probabilities from the probability distribution. Know how to tell whether two events are independent.
16. Find some poker probabilities. Use the "hypergeo" program. The deck has been modified, but the changes to the deck are given.
17. Decision Theory. The payoff table has been given to you. Create the opportunistic loss table. Then give the values and optimal action under each criteria.
18. Solve a game matrix, giving the optimal row and column strategies, and the value of the game. Use the "game" program. Then find the strategies and value under non-optimal conditions.
19. Markov chain problem. The transition matrix is given. Find the initial state matrix, another state matrix, and the steady state matrix.
20. Absorbing Markov chain problem. The transition matrix is given. Find the fundamental matrix F and the matrix FR. Find the number of transient states you should expect to be in before leaving the system and the probability of going from a particular transient state to an absorbing state.

## Notes

• The test is open notebook. Make sure that your notes are complete in the sections covered on the exam.
• Most of the questions are like those off of previous exams. It is adviseable to go through your old exams and find similar problems and make sure you have them corrected.
• The entire test is an individual test. There is no group portion.
• The questions on the exam appear in chapter order. Having your notes in order will help.
• Answer as much as you can without your notes. Once you start using your notes, your speed will go way down.
• Be sure to answer more points than you need to get your grade, just in case you miss some. That is, if you need 145 points to keep your B, answer more than 145 points worth of problems.
• I would certainly make sure this study guide is in your notebook.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total 6 6 6 5 5 5 9 12 10 15 15 10 8 10 16 16 10 12 12 12 200