Chapter 8: Study Guide

1. 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).
2. Given P(A), P(B), and P(A and B), find five probabilities. Identify as mutually exclusive, independent, and/or all inclusive. A joint probability distribution will be extremely useful.
3. Given conditional probabilities, find four probabilities. A joint probability distribution will be extremely useful.
4. You have two bags with different amounts of bills in them. There are seven 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 (1 problem), taking a bill out of bag 1 and putting into bag 2 and then drawing a bill out of bag 2 (2 problems), picking a bag at random and taking a bill from it (3 problems), dumping the bags together and then taking a bill (1 problem).
5. Work a Bayesian problem. This is similar to the pregnancy test problem 8.3.42 (pg 513) in the text.
6. 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 1-3) must be worked individually. The second page can be worked in groups of up to size three after the first page is turned in. You will want to bring scratch paper.

Last updated: Wednesday, July 19, 1995 at 7:25 am