MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS
8th Edition
ISBN: 9780357537343
Author: Johnson
Publisher: CENGAGE L
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Chapter 11.2, Problem 12E
To determine
The reason behind the description of Markov chain.
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5. Markov's Chains
Once a year employees at a company are given the opportunity to join one of three pension plans, A, B, or C. Once an employee decides to join one of these plans, the employee cannot drop the plan or switch to another plan. Past records indicate that each year 4% of the employees elect to join plan A, 14% elect to join plan B, 7% elect to join plan C, and the remainder do not join any plan.
(A) In the long run, what percentage of the employees will elect to join plan A? Plan B? Plan C?
(B) On the average, how many years will it take an employee to decide to join a plan?
A certain stock price has been observed to follow a pattern. If the stock price goes up one day, there's a 20% chance of it rising tomorrow, a 30% chance of it falling, and a 50% chance of it remaining the same. If the stock price falls one day, there's a 35% chance of it rising tomorrow, a 50% chance of it falling, and a 15% chance of it remaining the same. Finally, if the price is stable on one day, then it has a 50-50 change of rising or falling the next day. Find transition probability matrix for this Markov chain, if we list states in the order: (rising, falling, constant)
6. Suppose you are a broker (of junk bonds) who buys only bonds that have a 55% chance of not defaulting. You want to put together a portfolio of bonds with at least three that will not default. You want to be 95% sure that at least three will not default. How many bonds should you buy?
Chapter 11 Solutions
MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS
Ch. 11.0A - In Exercises 1-10, a find the dimensions of the...Ch. 11.0A - Prob. 2ECh. 11.0A - Prob. 3ECh. 11.0A - Prob. 4ECh. 11.0A - Prob. 5ECh. 11.0A - Prob. 6ECh. 11.0A - Prob. 7ECh. 11.0A - Prob. 8ECh. 11.0A - Prob. 9ECh. 11.0A - In Exercises 1-10, a find the dimensions of the...
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