Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
14th Edition
ISBN: 9780134677972
Author: Barnett
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 9, Problem 17RE
In Problems 17-20, use a graphing calculator to approximate the limiting matrix for the indicated transition matrix.
Matrix
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
y =
log
5
– x2
-
4
00
For what value of A and B the function f(x) will be continuous everywhere for the given definition?..
Please fill in the rest of the steps of the proof of Thm 2.5. Show how "Repeating this step with n-1,n-2,...,2 in place of n" gives us the desired result.
Chapter 9 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Ch. 9.1 - (A) Refer to the transition diagram in Figure 1....Ch. 9.1 - Refer to Example 4. States D and G are referred to...Ch. 9.1 - An insurance company classifies drivers as...Ch. 9.1 - Find P4 and use it to find S4 for AAP=AA.8.2.3.7...Ch. 9.1 - Use P8 and a graphing calculator to find S8 for P...Ch. 9.1 - Refer to Example 4. At the end of each year the...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...
Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - In Problems 9-14, use the transition matrix...Ch. 9.1 - In Problems 9-14, use the transition matrix...Ch. 9.1 - In Problems 9-14, use the transition matrix...Ch. 9.1 - In Problems 9-14, use the transition matrix...Ch. 9.1 - In Problems 9-14, use the transition matrix...Ch. 9.1 - In Problems 9-14, use the transition matrix...Ch. 9.1 - In Problems 15-20, use the transition diagram to...Ch. 9.1 - In Problems 15-20, use the transition diagram to...Ch. 9.1 - In Problems 15-20, use the transition diagram to...Ch. 9.1 - In Problems 15-20, use the transition diagram to...Ch. 9.1 - In Problems 15-20, use the transition diagram to...Ch. 9.1 - In Problems 15-20, use the transition diagram to...Ch. 9.1 - In Problems 21-26, use the transition matrix...Ch. 9.1 - In Problems 21-26, use the transition matrix...Ch. 9.1 - In Problems 21-26, use the transition matrix...Ch. 9.1 - In Problems 21-26, use the transition matrix...Ch. 9.1 - In Problems 21-26, use the transition matrix...Ch. 9.1 - In Problems 21-26, use the transition matrix...Ch. 9.1 - In Problems 27-32, use the transition diagram to...Ch. 9.1 - In Problems 27-32, use the transition diagram to...Ch. 9.1 - In Problems 27-32, use the transition diagram to...Ch. 9.1 - In Problems 27-32, use the transition diagram to...Ch. 9.1 - In Problems 27-32, use the transition diagram to...Ch. 9.1 - In Problems 27-32, use the transition diagram to...Ch. 9.1 - Draw the transition diagram that corresponds to...Ch. 9.1 - Find the transition matrix that corresponds to the...Ch. 9.1 - Draw the transition matrix that corresponds to the...Ch. 9.1 - Find the transition diagram that corresponds to...Ch. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - Prob. 42ECh. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - In Problems 45-50, is there a unique way of...Ch. 9.1 - In Problems 45-50, is there a unique way of...Ch. 9.1 - In Problems 45-50, is there a unique way of...Ch. 9.1 - In Problems 45-50, is there a unique way of...Ch. 9.1 - In Problems 45-50, is there a unique way of...Ch. 9.1 - In Problems 45-50, is there a unique way of...Ch. 9.1 - In Problems 51-56, are there unique values of a,b,...Ch. 9.1 - In Problems 51-56, are there unique values of a,b,...Ch. 9.1 - In Problems 51-56, are there unique values of a,b,...Ch. 9.1 - Prob. 54ECh. 9.1 - In Problems 51-56, are there unique values of a,b,...Ch. 9.1 - Prob. 56ECh. 9.1 - In Problems 57-60, use the given information to...Ch. 9.1 - A Markov chain has two states, A and B. The...Ch. 9.1 - Prob. 59ECh. 9.1 - Prob. 60ECh. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - Prob. 65ECh. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - Prob. 67ECh. 9.1 - Prob. 68ECh. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - In Problems 71-74, given the transition matrix P...Ch. 9.1 - In Problems 71-74, given the transition matrix P...Ch. 9.1 - In Problems 71-74, given the transition matrix P...Ch. 9.1 - In Problems 71-74, given the transition matrix P...Ch. 9.1 - A Markov chain with two states has transition...Ch. 9.1 - Repeat Problem 75 if the initial-state matrix is...Ch. 9.1 - Given the transition matrix...Ch. 9.1 - Prob. 78ECh. 9.1 - Show that if P=a1a1bb is probability matrix, then...Ch. 9.1 - Show that if P=a1a1bbandS=c1c are probability...Ch. 9.1 - Use a graphing calculator and the formula Sk =...Ch. 9.1 - Use a graphing calculator and the formula Sk=S0Pk...Ch. 9.1 - Use a graphing calculator and the formula Sk=S0Pk...Ch. 9.1 - Use a graphing calculator and the formula Sk=S0Pk...Ch. 9.1 - Scheduling. An outdoor restaurant in a summer...Ch. 9.1 - Scheduling. Repeat Problem 85 if the probability...Ch. 9.1 - Advertising. A television advertising campaign is...Ch. 9.1 - Car rental. A car rental agency has facilities at...Ch. 9.1 - Homeowner's insurance. In a given city, the market...Ch. 9.1 - Service contracts. A small community has two...Ch. 9.1 - Travel agent training. A chain of travel agencies...Ch. 9.1 - Welder training. All welders in a factory begin as...Ch. 9.1 - Health plans. A midwestern university offers its...Ch. 9.1 - Dental insurance. Refer to Problem 93. During the...Ch. 9.1 - Housing trends. The 2000 census reported that 41.9...Ch. 9.1 - Housing trends. The 2000 census reported that 66.4...Ch. 9.2 - (A) Suppose that the toothpaste company started...Ch. 9.2 - Which of the following matrices are regular? (A)...Ch. 9.2 - The transition matrix for a Markov chain is...Ch. 9.2 - Refer to Matched Problem 1 in Section 9.1, where...Ch. 9.2 - A mail-order company classifies its customers as...Ch. 9.2 - Repeat Example 5 for P=.3.6.1.2.3.5.1.2.7Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - Problems 31-34 refer to the regular Markov chain...Ch. 9.2 - Problems 31-34 refer to the regular Markov chain...Ch. 9.2 - Problems 31-34 refer to the regular Markov chain...Ch. 9.2 - Problems 31-34 refer to the regular Markov chain...Ch. 9.2 - In Problems 35-40, discuss the validity of each...Ch. 9.2 - In Problems 35-40, discuss the validity of each...Ch. 9.2 - In Problems 35-40, discuss the validity of each...Ch. 9.2 - In Problems 35-40, discuss the validity of each...Ch. 9.2 - In Problems 35-40, discuss the validity of each...Ch. 9.2 - In Problems 35-40, discuss the validity of each...Ch. 9.2 - In Problems 41-44, approximate the stationary...Ch. 9.2 - In Problems 41-44, approximate the stationary...Ch. 9.2 - In Problems 41-44, approximate the stationary...Ch. 9.2 - In Problems 41-44, approximate the stationary'...Ch. 9.2 - A red urn contains 2 red marbles and 3 blue...Ch. 9.2 - Repeat Problem 45 if the red urn contains 5 red...Ch. 9.2 - Given the transition matrix P=0110 A) Discuss the...Ch. 9.2 - Given the transition matrix P=001100010 (A)...Ch. 9.2 - The transition matrix for a Markov chain is...Ch. 9.2 - The transition matrix for a Markov chain is...Ch. 9.2 - Problems 51 and 52 require the use of a graphing...Ch. 9.2 - Problems 51 and 52 require the use of a graphing...Ch. 9.2 - The transition matric for a Markov chain is...Ch. 9.2 - The transition matric for a Markov chain is...Ch. 9.2 - Transportation. Most railroad cars are owned by...Ch. 9.2 - Transportation. The railroad in Problem 55 also...Ch. 9.2 - Labor force. Table 1 gives the percentage of the...Ch. 9.2 - Home ownership. The U.S. Census Bureau published...Ch. 9.2 - Market share. Consumers can choose between three...Ch. 9.2 - Market share. Consumers in a certain area can...Ch. 9.2 - Insurance. An auto insurance company classifies...Ch. 9.2 - Insurance. Repeat Problems 61 if 40 of preferred...Ch. 9.2 - Problems 63 and 64 require the use of a graphing...Ch. 9.2 - Problems 63 and 64 require the use of a graphing...Ch. 9.2 - Genetics. A given plant species has red, pink, or...Ch. 9.2 - Gene mutation. Suppose that a gene in a chromosome...Ch. 9.2 - Rapid transit. A new rapid transit system has just...Ch. 9.2 - Politics: filibuster. The Senate is in the middle...Ch. 9.2 - The population center of the 48 contiguous states...Ch. 9.2 - The population center of the 48 contiguous states...Ch. 9.3 - (A) For the initial-state matrix S0=abc, find the...Ch. 9.3 - Determine whether each statement is true or false....Ch. 9.3 - Identify any absorbing states for the following...Ch. 9.3 - Use a transition diagram to determine whether P is...Ch. 9.3 - Repeat Example 3 if 10 of farmers sell to company...Ch. 9.3 - Repeat Example 4 for the standard form P found in...Ch. 9.3 - Repeat Example 5 for the following transition...Ch. 9.3 - In Problems 1-6, identify the absorbing states in...Ch. 9.3 - In Problems 1-6, identify the absorbing states in...Ch. 9.3 - In Problems 1-6, identify the absorbing states in...Ch. 9.3 - In Problems 1-6, identify the absorbing states in...Ch. 9.3 - In Problems 1-6, identify the absorbing states in...Ch. 9.3 - In Problems 1-6, identify the absorbing states in...Ch. 9.3 - In Problems 7-10, identify the absorbing states...Ch. 9.3 - In Problems 7-10, identify the absorbing states...Ch. 9.3 - In Problems 7-10, identify the absorbing states...Ch. 9.3 - In Problems 7-10, identify the absorbing states...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 21-24.find a standard form for the...Ch. 9.3 - In Problems 21-24.find a standard form for the...Ch. 9.3 - In Problems 21-24.find a standard form for the...Ch. 9.3 - In Problems 21-24.find a standard form for the...Ch. 9.3 - In Problems 25-28, find a standard form for the...Ch. 9.3 - In Problems 25-28, find a standard form for the...Ch. 9.3 - In Problems 25-28, find a standard form for the...Ch. 9.3 - In Problems 25-28, find a standard form for the...Ch. 9.3 - In Problems 29-34, find the limiting matrix for...Ch. 9.3 - In Problems 29-34, find the limiting matrix for...Ch. 9.3 - In Problems 29-34, find the limiting matrix for...Ch. 9.3 - In Problems 29-34, find the limiting matrix for...Ch. 9.3 - In Problems 29-34, find the limiting matrix for...Ch. 9.3 - In Problems 29-34, find the limiting matrix for...Ch. 9.3 - Problems 35-40 refer to the matrices in Problems...Ch. 9.3 - Problems 35-40 refer to the matrices in Problems...Ch. 9.3 - Problems 35-40 refer to the matrices in Problems...Ch. 9.3 - Problems 35-40 refer to the matrices in Problems...Ch. 9.3 - Problems 35-40 refer to the matrices in Problems...Ch. 9.3 - Problems 35-40 refer to the matrices in Problems...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 49-52, use a graphing calculator to...Ch. 9.3 - In Problems 49-52, use a graphing calculator to...Ch. 9.3 - In Problems 49-52, use a graphing calculator to...Ch. 9.3 - In Problems 49-52, use a graphing calculator to...Ch. 9.3 - The following matrix P is a nonstandard transition...Ch. 9.3 - Repeat Problem 53 for...Ch. 9.3 - Verify the results in Problem 53 by computing Pk...Ch. 9.3 - Verify the results in Problem 54 by computing Pk...Ch. 9.3 - Show that S=x1x0,0x1, is a stationary matrix for...Ch. 9.3 - Show that S=x1x00,0x1, is a stationary matrix for...Ch. 9.3 - An absorbing Markov chain has the following matrix...Ch. 9.3 - Refer to the matrices P and Q of Problem 59. For k...Ch. 9.3 - Loans. A credit union classifies car loans into...Ch. 9.3 - Employee training. A chain of car muffler and...Ch. 9.3 - Marketing. Three electronics firms are...Ch. 9.3 - Pensions. Once a year company employees are given...Ch. 9.3 - Medicine. After bypass surgery, patients are...Ch. 9.3 - Medicine. The study discussed in Problem 65 also...Ch. 9.3 - Psychology. A rat is placed in room F or room B of...Ch. 9.3 - Psychology. Repeat Problem 67 if the exit from...Ch. 9 - Given the transition matrix P and initial-state...Ch. 9 - In Problems 2-6, P is a transition matrix for a...Ch. 9 - In Problems 2-6, P is a transition matrix for a...Ch. 9 - In Problems 2-6, P is a transition matrix for a...Ch. 9 - In Problems 2-6, P is a transition matrix for a...Ch. 9 - Prob. 6RECh. 9 - In Problems 7-10, write a transition matrix for...Ch. 9 - In Problems 7-10, write a transition matrix for...Ch. 9 - In Problems 7-10, write a transition matrix for...Ch. 9 - In Problems 7-10, write a transition matrix for...Ch. 9 - A Markov chain has three states, A,B, and C. The...Ch. 9 - Given the transition matrix ABP=AB.4.6.9.1 find...Ch. 9 - In Problems 13 and 14. solve the equation SP=S to...Ch. 9 - In Problems 13 and 14. solve the equation SP=S to...Ch. 9 - In Problems 15 and 16, find the limiting matrix...Ch. 9 - In Problems 15 and 16, find the limiting matrix...Ch. 9 - In Problems 17-20, use a graphing calculator to...Ch. 9 - In Problems 17-20, use a graphing calculator to...Ch. 9 - In Problems 17-20, use a graphing calculator to...Ch. 9 - In Problems 17-20, use a graphing calculator to...Ch. 9 - Find a standard form for the absorbing Markov...Ch. 9 - In Problems 22 and 23, determine the long-run...Ch. 9 - In Problems 22 and 23, determine the long-run...Ch. 9 - Let P be a 22 transition matrix for a Markov...Ch. 9 - Let P be a 33 transition matrix for a Markov...Ch. 9 - A red urn contains 2 red marbles, 1 blue marble,...Ch. 9 - Repeat Problem 26 if the blue and green marbles...Ch. 9 - Show that S=xyz0, where 0x1, 0y1, 0z1, and...Ch. 9 - Give an example of a transition matrix for a...Ch. 9 - Give an example of a transition matrix for an...Ch. 9 - Give an example of a transition matrix for a...Ch. 9 - Give an example of a transition matrix for an...Ch. 9 - Explain why an absorbing Markov chain that has...Ch. 9 - Explain why a regular Markov chain that has more...Ch. 9 - A Markov chain has transition matrix P=.4.6.2.8...Ch. 9 - In Problems 36 and 37, use a graphing calculator...Ch. 9 - In Problems 36 and 37, use a graphing calculator...Ch. 9 - Product switching. A company's brand X has 20 of...Ch. 9 - Marketing. Recent technological advances have led...Ch. 9 - Prob. 40RECh. 9 - Employee training. In order to become a fellow of...Ch. 9 - Genetics. A given plant species has red, pink, or...Ch. 9 - Smoking. Table 2 gives the percentage of U.S....
Additional Math Textbook Solutions
Find more solutions based on key concepts
In hypothesis testing, the common level of significance is =0.05. Some might argue for a level of significance ...
Basic Business Statistics, Student Value Edition
Fill in each blank so that the resulting statement is true. An equation that expresses a relationship between t...
Algebra and Trigonometry (6th Edition)
Find the derivatives of the functions in Exercises 23–50.
43.
University Calculus: Early Transcendentals (4th Edition)
Explain the meaning of the term “statistically significant difference” in statistics terminology.
Intro Stats, Books a la Carte Edition (5th Edition)
The equivalent expression of x(y+z) by using the commutative property.
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Mathematical Connections Explain why 25 cents is one-fourth of a dollar, yet 15 minutes is one-fourth of an hou...
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- 2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.006.MI. Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 7y2 y² 11 dy Need Help? Read It Master It SUBMIT ANSWER 3. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.009. Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) tan³(12/z) dz Need Help? Read It Watch It SUBMIT ANSWER 4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.014. Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 5 sinб12x dx Need Help? Read Itarrow_forwardPlease refer belowarrow_forwardy"-9y+20y= 80t-156 y(0) = −6, y'(0) = 5 y(t) =arrow_forward
- Please refer belowarrow_forwardHi, can you guys help me with this? Thank you! Can you guys help me calculate again the Term GPA, Combined GPA, Cumulative GPA, Transfer GPA & Combined Cumulative GPA section? It's just not right right now. Here's the transfer totals point that I want to provide just in case you guys may ask where I get these from:arrow_forwardUse undetermined coefficients to find the particular solution to y"-3y+2y=4e3 Y(t) =arrow_forward
- Please refer belowarrow_forwardUse undetermined coefficients to find the particular solution to y"-y+5y = 7t² +61 +3 Yp(t) =arrow_forwardConsider the initial value problem y"+y'-12y= 0, y(0) = a, y'(0) = 4 Find the value of a so that the solution to the initial value problem approaches zero as too a =arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSON
Discrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Finite Math: Markov Chain Example - The Gambler's Ruin; Author: Brandon Foltz;https://www.youtube.com/watch?v=afIhgiHVnj0;License: Standard YouTube License, CC-BY
Introduction: MARKOV PROCESS And MARKOV CHAINS // Short Lecture // Linear Algebra; Author: AfterMath;https://www.youtube.com/watch?v=qK-PUTuUSpw;License: Standard Youtube License
Stochastic process and Markov Chain Model | Transition Probability Matrix (TPM); Author: Dr. Harish Garg;https://www.youtube.com/watch?v=sb4jo4P4ZLI;License: Standard YouTube License, CC-BY