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7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337274203

Chapter 8.7, Problem 54E

Textbook Problem

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**Dissipation with Drift** Consider the following five-state model of one-dimensional dissipation with drift:

Find the steady-state distribution vector.

To determine

**To calculate:** The steady-state distribution vector with the help of five-state model of one-dimensional dissipation with drift as shown in figure,

**Given information:**

The five-state model of one-dimensional dissipation with drift is shown in figure,

**Formula Used:**

To calculate the steady-state probability vector for a Markov system for transition probability matrix *P*, solve the system of equations,

The steady-state vector is,

**Calculation:**

Consider the diagram,

With the help of the above diagram, the transition matrix can be formed as,

Now, the steady-state vectors from the above matrix are as,

And,

Solve for the system and rewrite the above equations in standard form and drop the last equation as,

Finite Mathematics and Applied Calculus (MindTap Course List)

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In Exercises 6368, draw an appropriate tree...Ch. 8.5 - In Exercises 6368, draw an appropriate tree...Ch. 8.5 - In Exercises 6368, draw an appropriate tree...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Education and Employment Exercises 6978 are based...Ch. 8.5 - Air Bag Safety According to a 2000 study conducted...Ch. 8.5 - Air Bag Safety According to the study cited in...Ch. 8.5 - Productivity A company wishes to enhance...Ch. 8.5 - Productivity Consider the events T and I in...Ch. 8.5 - 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Cyber Video...Ch. 8.5 - The probability of misspelling Waner is p and is...Ch. 8.5 - The probability of spelling Waner correctly is p,...Ch. 8.5 - Name three events, each independent of the others,...Ch. 8.5 - Name three pairs of independent events when a pair...Ch. 8.5 - You wish to ascertain the probability of an event...Ch. 8.5 - Your television advertising campaign seems to have...Ch. 8.5 - You are having trouble persuading your friend...Ch. 8.5 - Your other friend Giuseppe is spreading rumors...Ch. 8.5 - If AB and P(B)0, why is P(A|B)=P(A)P(B)?Ch. 8.5 - If BA and P(B)0, why is P(A|B)=1?Ch. 8.5 - Your best friend thinks that it is impossible for...Ch. 8.5 - Another of your friends thinks that two mutually...Ch. 8.5 - Show that if A and B are independent, then so are...Ch. 8.5 - Show that if A and B are independent, then so are...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - In Exercises 18, use Bayes theorem or a tree...Ch. 8.6 - Music Downloading According to a study on the...Ch. 8.6 - Music Downloading According to the study cited in...Ch. 8.6 - Weather It snows in Greenland an average of once...Ch. 8.6 - Weather It rains in Spain an average of once every...Ch. 8.6 - University Admissions In fall 2014, 34% of...Ch. 8.6 - University Admissions In fall 2014, 71% of...Ch. 8.6 - Side-Impact Hazard In 2004, 45.4% of all light...Ch. 8.6 - Side-Impact Hazard In 2004, 27.3% of all light...Ch. 8.6 - Athletic Fitness Tests Any athlete who fails the...Ch. 8.6 - Academic Testing Professor Frank Nabarro insists...Ch. 8.6 - Side-Impact Hazard (Compare Exercise 15.) In 2004,...Ch. 8.6 - Side-Impact Hazard In 1986, 23.9% of all light...Ch. 8.6 - University Admissions In fall 2008, UCLA admitted...Ch. 8.6 - University Admissions In fall 2002, UCLA admitted...Ch. 8.6 - Internet Use (Historical) In 2000, 86% of all...Ch. 8.6 - Internet Use (Historical) In 2000, 59% of all...Ch. 8.6 - Market Surveys A New York Times survey of...Ch. 8.6 - Crime and Preschool. A New York Times survey82 of...Ch. 8.6 - Grade Complaints Two of the mathematics professors...Ch. 8.6 - Weather Prediction A local TV station employs...Ch. 8.6 - Employment in the 1980s In a 1987 survey of...Ch. 8.6 - Employment in the 1980s Repeat Exercise 29 in the...Ch. 8.6 - Juvenile Delinquency According to a study at the...Ch. 8.6 - Crime According to the same study at the Oregon...Ch. 8.6 - Benefits of Exercise According to a study in The...Ch. 8.6 - Benefits of Exercise Repeat Exercise 33 assuming...Ch. 8.6 - Air Bag Safety According to a 2000 study conducted...Ch. 8.6 - Air BagSafety According to the study cited in...Ch. 8.6 - Your friend claims that the probability of A given...Ch. 8.6 - Complete the following sentence. To use Bayes...Ch. 8.6 - Give an example in which a steroids test gives a...Ch. 8.6 - Give an example in which a steroids test gives a...Ch. 8.6 - Use a tree to derive the expanded form of Bayes...Ch. 8.6 - Write down an expanded form of Bayes theorem that...Ch. 8.6 - Politics The following letter appeared in The New...Ch. 8.6 - Politics Refer back to Exercise 43. If the letter...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 110, write down the transition matrix...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 1124, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - In Exercises 2536, you are given a transition...Ch. 8.7 - Marketing A market survey shows that half the...Ch. 8.7 - Major Switching At Suburban Community College, 10%...Ch. 8.7 - Pest Control In an experiment to test the...Ch. 8.7 - Employment You have worked for the Department of...Ch. 8.7 - Risk Analysis An auto insurance company classifies...Ch. 8.7 - Debt Analysis A credit card company classifies its...Ch. 8.7 - Textbook Adoptions College instructors who adopt...Ch. 8.7 - Confidence Level Tommy the Dunkers performance on...Ch. 8.7 - Debt Analysis As the manager of a large retailing...Ch. 8.7 - Debt Analysis Repeat Exercise 45 using the...Ch. 8.7 - Market Share: Cell Phones Three of the largest...Ch. 8.7 - Dissipation Consider the following five-state...Ch. 8.7 - Dissipation with Drift Consider the following...Ch. 8.7 - Describe an interesting situation that can be...Ch. 8.7 - Describe an interesting situation that can be...Ch. 8.7 - Describe some drawbacks to using Markov processes...Ch. 8.7 - Can the repeated toss of a fair coin be modeled by...Ch. 8.7 - Explain: If Q is a matrix whose rows are...Ch. 8.7 - Construct a four-state Markov system so that both...Ch. 8.7 - Refer to the following state transition diagram,...Ch. 8.7 - Without doing any calculation, find the...Ch. 8.7 - Construct a regular state transition diagram that...Ch. 8.7 - Construct a regular state transition diagram that...Ch. 8.7 - Show that if a Markov system has two distinct...Ch. 8.7 - If higher and higher powers of P approach a fixed...Ch. 8 - In Exercises 16, say how many elements are in the...Ch. 8 - In Exercises 16, say how many elements are in the...Ch. 8 - In Exercises 16, say how many elements are in the...Ch. 8 - In Exercises 16, say how many elements are in the...Ch. 8 - In Exercises 16, say how many elements are in the...Ch. 8 - In Exercises 16, say how many elements are in the...Ch. 8 - In Exercises 710, calculate the relative frequency...Ch. 8 - In Exercises 710, calculate the relative frequency...Ch. 8 - In Exercises 710, calculate the relative frequency...Ch. 8 - In Exercises 710, calculate the relative frequency...Ch. 8 - In Exercises 1114, calculate the probability P(E)....Ch. 8 - In Exercises 1114, calculate the probability P(E)....Ch. 8 - In Exercises 1114, calculate the probability P(E)....Ch. 8 - In Exercises 1114, calculate the probability P(E)....Ch. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - A bag contains four red marbles, two green ones,...Ch. 8 - In Exercises 2126, find the probability of being...Ch. 8 - In Exercises 2126, find the probability of being...Ch. 8 - In Exercises 2126, find the probability of being...Ch. 8 - In Exercises 2126, find the probability of being...Ch. 8 - In Exercises 2126, find the probability of being...Ch. 8 - In Exercises 2126, find the probability of being...Ch. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - Two dice, one green and one yellow, are rolled. In...Ch. 8 - A poll shows that half the consumers who use Brand...Ch. 8 - A poll shows that half the consumers who use Brand...Ch. 8 - A poll shows that half the consumers who use Brand...Ch. 8 - A poll shows that half the consumers who use Brand...Ch. 8 - Inventory OHaganBooks.com currently operates three...Ch. 8 - Inventory OHaganBooks.com currently operates three...Ch. 8 - Inventory OHaganBooks.com currently operates three...Ch. 8 - Inventory OHaganBooks.com currently operates three...Ch. 8 - Inventory OHaganBooks.com currently operates three...Ch. 8 - Inventory OHaganBooks.com currently operates three...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Marketing To gauge the effectiveness of the...Ch. 8 - Sales According to statistics gathered by...Ch. 8 - Sales Repeat Exercise 51 in the event that 1% of...Ch. 8 - University Admissions In the year when Billy-Sean...Ch. 8 - University Admissions Billy-Sean OHagan had also...Ch. 8 - Competition As was mentioned earlier,...Ch. 8 - Competition As was mentioned earlier,...Ch. 8 - Competition As was mentioned earlier,...Ch. 8 - Competition As was mentioned earlier,...

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