11th Edition

ISBN: 9780321979438

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

Publisher: PEARSON

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Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.

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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axi…

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between…

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Textbook Question

Chapter 10.1, Problem 1E

Decide whether each matrix could be a probability vector.

[ 2 3 1 2 ]

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Chapter 9, Problem 59RE

Chapter 10.1, Problem 2E

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In this exercise, we will investigate a technique to prove that a language is notregular. This tool is called the pumping lemma.The pumping lemma says that if M = (S, I, f, s0, F ) is a DFA with p states (i.e., p = |S|) and if the wordw is in L(M ) (the language generated by M ) and w has length greater than or equal to p, then w may bedivided into three pieces, w = xyz, satisfying the following conditions:1. For each i ∈ N, xy^i z ∈ L(M ).2. |y| > 0 (i.e., y contains at least one character).3. |xy| ≤ p (i.e., the string xy has at most p characters). Use the pumping lemma to show the following language is not regular (HINT: Use proof by contradictionto assume the language is regular and apply the pumping lemma to the language):L = {0^k1^k | k ∈ N}

A prefix of length ℓ of some word w are the first ℓ characters (in order) of w.1. Construct a context-free grammar for the language: L = {w ∈ {a, b}∗ | every prefix of w has at least as many a’s as b’s}2. Explain why every word generated by your context-free grammar (in Part 1) is contained in L. Then,prove via induction that every w ∈ L is produced by your context-free grammar.

Consider a simplified version of American football where on any possession ateam can earn 0, 3 or 7 points. What is the smallest number n0 of points such that for all n ≥ n0 and n ∈ Na team could earn n points. You must prove that your answer is correct via induction (HINT: Don’t forgetto show that n0 is the smallest number above which any number of points is reachable).

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. Which...Ch. 10 - Prob. 37RE Ch. 10 - Prob. 38RE Ch. 10 - Prob. 39RE Ch. 10 - Prob. 40RE Ch. 10 - Prob. 41RE Ch. 10 - Prob. 42RE Ch. 10 - Prob. 43RE Ch. 10 - Prob. 44RE Ch. 10 - Prob. 45RE Ch. 10 - Prob. 46RE Ch. 10 - Prob. 47RE Ch. 10 - Prob. 48RE Ch. 10 - Life Sciences 49. Medical Prognosis A study...Ch. 10 - Prob. 50RE Ch. 10 - Prob. 51RE Ch. 10 - Prob. 52RE Ch. 10 - Prob. 53RE Ch. 10 - Prob. 54RE Ch. 10 - Prob. 55RE Ch. 10 - Prob. 56RE Ch. 10 - Prob. 57RE Ch. 10 - Prob. 58RE Ch. 10 - Prob. 59RE Ch. 10 - Prob. 60RE Ch. 10 - Prob. 61RE Ch. 10 - Prob. 62RE Ch. 10 - Prob. 63RE Ch. 10 - Prob. 64RE Ch. 10 - Prob. 65RE Ch. 10 - Prob. 66RE Ch. 10 - Prob. 67RE Ch. 10 - Prob. 68RE Ch. 10 - 69. Gambling Suppose a casino offers a gambling...

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Decide whether each matrix could be a probability vector . l. [ 2 3 1 2 ]

Solution Summary: The author explains that the provided vector is not a probability vector if the following conditions hold.

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