Math 160 - Projects






Project 1, Chapter 3

Part I (10 points) - Individual

Your project is to plan a retirement fund for yourself. To simplify calculations, assume all transactions - starting of annuity fund, retirement, and death - occur on your birthday. Assume a nominal interest rate of 3% has been guaranteed for the remainder of your life. There is a financial planning worksheet to give you an idea of the format I'm looking for. Feel free to use that paper to write your answers on.


Part II (10 points) - Group


  2. How much is the down payment?
  5. How much interest will you pay?
    2. How much is the house worth if it is now worth 8% more than what you paid for it?
    3. How much equity do you have in the house?
    2. How much will you repay
    3. How much interest will you pay?

Project 2, Chapter 4

Part I - Dominance Relation (10 points)

Open the national_league_2010.wxm file within wxMaxima and read the instructions. (You will need to right click and save the file).

In an effort to predict the rankings for the 2011 season a bookie awards as follows (the overall score is the total of the three scores).

  1. Write a matrix expression that can be used to find the overall score for each team.
  2. How many points did New York Mets directly receive from the San Francisco Giants?
  3. How many total points did Chicago Cubs receive from the Cincinnati Reds?
  4. List the teams and their overall scores.
  5. Write a matrix expression that can be used to determine how many games each team won. Which team won the most games?
  6. Write a matrix expression that can be used to determine which team lost the most games. Which team was that?

Part II - The Internet2 (10 points)

The Internet2 is a high-speed network for the U.S. research and education community. The network is connected through Internet2 Router sites, located in 9 cities throughout the United States. There is a map of the Internet2 network at

There is a blank incidence matrix that you may wish to print and use to make this easier for you. In the following, "hop" or "network segment", means a trip between two cities.

  1. Create an incidence matrix for the Internet2 router sites (all traffic is bi-directional). List the cities in alphabetical order.
  2. What is the maximum number of hops a packet might require before reaching its destination? (Hint: find A+A2+A3+…+An until every non-diagonal element is greater than zero). Write down this matrix.
  3. Part of the design of a good network is redundancy. If any one site loses connectivity, the rest of the network must continue to function. If the site at Kansas City goes down, what is the maximum number of hops a packet might require before reaching its destination (assume its destination isn't Kansas City)? Write down the matrix used to determine this answer.

I also strongly recommend using Maxima or similar computer program to find your answers. If you don't want to write the answers down by hand into the incidence matrices, you can copy the output from Maxima into Word and then print that. However, you will need to manually label the rows and columns if you do that.

Project 3, Chapter 8

Part I - Poker Probabilities (5 points)


  1. Four of a Kind
  2. Full House - (Three of one kind of card and two of another)
  3. Three of a Kind
  4. Two Pairs
  5. One Pair

Part II - Illinois Lottery (5 points)

Use the information on the Illinois Lottery website to answer this part. The rules and the chances of winning are given on the website. The chances of winning are given on the website, so it is important that you show the work necessary to arrive at the answer. Find the probabilities that a ticket will win the following prizes. (Hint: Think of the Mega Millions game as a combination of two separate games, each using a hypergeometric distribution).

  1. Mega Millions game, second prize
  2. Mega Millions game, third prize
  3. Mega Millions game, fourth prize
  4. Lotto, second prize
  5. Lotto, third prize

Part III - Decision Theory (10 points)


  1. Create a payoff table with the five actions (remember that you can combine purchases from more than one dealer and some plans don't make any sense when the demand is considered) and four states of nature (demand)
  2. Create the opportunistic loss (regret) table.

Project 4, Chapter 9

Part I - Peg Moving (10 points)


  1. Create a transition matrix.
  2. Find the fundamental matrix F.

Part II - Craps (10 points)



  4. Find the expected number of rolls for a game of craps. To find the expected number of rolls for a point (since they're different depending on the point value), find the expected value of the number of rolls when weighted with the probability of rolling that point. Be sure and add one to the number of rolls to include the first roll of the dice.

Project 5, Chapter 10

Part I (10 points)

Consider the following two-person zero-sum game.

  Cereal Dairy Meat Snacks
Baking -3 1 -5 4
Fruits 2 -1 -2 3
Pasta -1 1 3 -2
Soda 3 4 -1 2



Answer the following questions.

  1. If Rick and Corissa each randomly select a food type to put on sale, what are the strategies and what is the value of the game for Rick?
  2. What are the optimal strategies for Rick and Corissa? What is the value of the game for Rick under that those strategies?
  3. Find the expected payoff values for each of Rick's actions if Corissa plays her optimal strategies. Find the expected loss values for each of Corissa's actions if Rick plays his optimal strategies.
    1. What is the expected value of each action for Rick?
    2. What should Rick's a priori strategy be using the expected value criterion?
    3. What should Corissa's strategy really be (not what she said) if the intent was to trick Rick into playing a particular strategy?

Part II (10 points)

  3. Solve the game using the calculator.