- Use the multiplication rule involving combinations. This could be a hypergeometric problem.
- Find the number of ways a specific set of officers can be elected.
- Find the total frequency given the empirical probability and observed frequency.
- Find the probabilities of five poker hands.
- Play a game. Create the sample space. Write a probability distribution based on the sample space. Find the expected value. Identify the game as fair or not. Decide whether the person should play or not.
- Work a decision theory problem. Complete the payoff table. Find the opportunistic loss (regret) table. Find the expected value under each action and the best action under each principle (expected value, maximin, maximax, minimax).
- Markov chain mouse problem. Determine the initial state matrix, the transition matrix, and the log term probabilities of being in each state (steady state matrix). Also determine the probability after the first move (can be done without matrices).
- You have two bags with different amounts of bills in them. There are five situations presented, and you need to find the probability of each occurring. The situations include drawing a bill from both bags and looking at the sum, taking a bill out of bag 1 and putting into bag 2 and then drawing a bill out of bag 2 (2 parts), picking a bag at random and taking a bill from it, dumping the bags together and then taking a bill.
- Work a Bayesian problem. This is similar to the pregnancy test problem 8.3.42 (pg 513) in the text.
- A game is interrupted before completion. Decide what portion of the prize money should go to each player. As an example, look at problem 8.2.42 (pg 501). Extend it to like 4 sets that must be won instead of only 2. Assume Ann has won 3 sets and Barbara has won 1. Find the probability of Ann winning and Barbara winning (given that Ann has won 3 and Barbara 1 set). Ann receives the portion of the total equal to her probability of winning, and likewise for Barbara.

The first page, problems 1 - 4, must be worked individually. The remainder of the exam may be worked in groups of up to size three. You must turn in the first page before getting together to work in groups.

Last updated: Sunday, July 7, 1996 at 6:53 PM

Send comments to james@richland.edu.