11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

Concept explainers

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known …

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosi…

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the prob…

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Textbook Question

Chapter 10.3, Problem 32E

Tennis Consider a game of tennis when each player has won at least two serves. After that, the first player to win two serves more than his opponent wins. There are live possibilities: Either the players are tied (deuce), the server is a point ahead (ad in ), the other player is a point ahead (ad out), the server wins, or the server loses. If we assume that at each serve the server has a probability p of winning the next point, then the game can be modeled by a Markov chain. Source: The Mathematics Teacher.

(a) Verify that the transition matrix from the server's point of view is given by

Chapter 10.3, Problem 32E,

32. Tennis Consider a game of tennis when each player has won at least two serves. After that, the

(b) For the case in which p = 0.6 find the probability that the server will win when the score is ad out, deuce, and ad in.

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Chapter 10.3, Problem 31E

Chapter 10.3, Problem 33E

Chapter 10 Solutions

Finite Mathematics (11th Edition)

Ch. 10.1 - Decide whether each matrix could be a...Ch. 10.1 - Decide whether each matrix could be a probability...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Decide whether each matrix could be a probability...Ch. 10.1 - Decide whether each matrix could be a...Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Decide whether each matrix could be a transition...Ch. 10.1 - Decide whether each matrix could be a...

Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - In Exercises and 16, write each transition diagram...Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Find the first three powers of each transition...Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Insurance An insurance company classifies its...Ch. 10.1 - Insurance The difficulty with the mathematical...Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - 32. Land Use In one state, a Board of Realtors...Ch. 10.1 - Business The change in the size of businesses in a...Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Housing Patterns In a survey investigating changes...Ch. 10.1 - Migration A study found that the way people living...Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.2 - Which of the following transition matrices are...Ch. 10.2 - Which of the following transition matrices are...Ch. 10.2 - Which of the following transition matrices are...Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Find the equilibrium vector for each transition...Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Find the equilibrium vector for each transition...Ch. 10.2 - Prob. 16E Ch. 10.2 - Find the equilibrium vector for each...Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - Prob. 21E Ch. 10.2 - Prob. 22E Ch. 10.2 - Prob. 23E Ch. 10.2 - Prob. 24E Ch. 10.2 - Business and Economics Quality Control The...Ch. 10.2 - 26. Quality Control Suppose improvements are made...Ch. 10.2 - (a) Dry Cleaning Using the initial probability...Ch. 10.2 - Mortgage Refinancing In 2009, many homeowners...Ch. 10.2 - Prob. 29E Ch. 10.2 - Prob. 30E Ch. 10.2 - Prob. 31E Ch. 10.2 - Prob. 32E Ch. 10.2 - Prob. 33E Ch. 10.2 - Prob. 34E Ch. 10.2 - Migration As we saw in the last section, a study...Ch. 10.2 - 36. Criminology A study male criminals in...Ch. 10.2 - Prob. 37E Ch. 10.2 - Prob. 38E Ch. 10.2 - Prob. 39E Ch. 10.2 - Prob. 40E Ch. 10.2 - Prob. 41E Ch. 10.2 - 42. Language One of Markov's own applications...Ch. 10.2 - Prob. 43E Ch. 10.2 - Prob. 44E Ch. 10.3 - Find all absorbing states for each transition...Ch. 10.3 - Find all absorbing states for each transition...Ch. 10.3 - Find all absorbing states for each transition...Ch. 10.3 - Find all absorbing states for each transition...Ch. 10.3 - Find all absorbing states for each transition...Ch. 10.3 - Find all absorbing states for each transition...Ch. 10.3 - Prob. 7E Ch. 10.3 - Prob. 8E Ch. 10.3 - Find the fundamental matrix F for the absorbing...Ch. 10.3 - Prob. 10E Ch. 10.3 - Find the fundamental matrix F for the absorbing...Ch. 10.3 - Find the fundamental matrix F for the absorbing...Ch. 10.3 - Prob. 13E Ch. 10.3 - Prob. 14E Ch. 10.3 - (a) Write a transition matrix for a gambler's ruin...Ch. 10.3 - Prob. 16E Ch. 10.3 - Prob. 17E Ch. 10.3 - Prob. 18E Ch. 10.3 - Prob. 19E Ch. 10.3 - 20. How can we calculate the expected total...Ch. 10.3 - Prob. 21E Ch. 10.3 - Prob. 22E Ch. 10.3 - Business and Economics 23. Solar Energy In...Ch. 10.3 - 24. Company Training Program A company with a...Ch. 10.3 - Contagion Under certain conditions, the...Ch. 10.3 - 26. Medical Prognosis A study using Markov chains...Ch. 10.3 - Prob. 27E Ch. 10.3 - Prob. 28E Ch. 10.3 - Prob. 29E Ch. 10.3 - Prob. 30E Ch. 10.3 - Gambler's Ruin (a) Write a transition matrix tor a...Ch. 10.3 - 32. Tennis Consider a game of tennis when each...Ch. 10.3 - Professional Football In Exercise 40 of the first....Ch. 10 - 1. If a teacher is currently ill, what is the...Ch. 10 - Prob. 2EA Ch. 10 - Prob. 3EA Ch. 10 - Prob. 4EA Ch. 10 - Prob. 5EA Ch. 10 - Prob. 6EA Ch. 10 - Prob. 7EA Ch. 10 - Prob. 1RE Ch. 10 - Prob. 2RE Ch. 10 - Prob. 3RE Ch. 10 - Prob. 4RE Ch. 10 - Prob. 5RE Ch. 10 - Prob. 6RE Ch. 10 - Prob. 7RE Ch. 10 - Prob. 8RE Ch. 10 - Prob. 9RE Ch. 10 - Prob. 10RE Ch. 10 - Prob. 11RE Ch. 10 - Prob. 12RE Ch. 10 - Prob. 13RE Ch. 10 - Prob. 14RE Ch. 10 - Prob. 15RE Ch. 10 - Prob. 16RE Ch. 10 - Prob. 17RE Ch. 10 - Prob. 18RE Ch. 10 - Prob. 19RE Ch. 10 - Prob. 20RE Ch. 10 - Prob. 21RE Ch. 10 - Prob. 22RE Ch. 10 - Prob. 23RE Ch. 10 - Prob. 24RE Ch. 10 - Prob. 25RE Ch. 10 - In Exercises 23-26, use the transition matrix P,...Ch. 10 - Prob. 27RE Ch. 10 - Prob. 28RE Ch. 10 - Prob. 29RE Ch. 10 - Decide whether each transition matrix is regular....Ch. 10 - Prob. 31RE Ch. 10 - Prob. 32RE Ch. 10 - Prob. 33RE Ch. 10 - Prob. 34RE Ch. 10 - Prob. 35RE Ch. 10 - Find all absorbing states for each matrix. 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Solution Summary: The author explains how the transition matrix can be modeled by a Markov chain.

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