The transition matrix for an absorbing Markov chain is shown below. PQRS r0.1 0 0 0.21 0.3 1 0 0.2 R 0.1 0 1 0.2 Lo.5 0 0 0.4 a) Rewrite this transition matrix in standard form. b) Find the fundamental matrix, F c) If a person starts in state P, on average, how many transitions will they remain in state P? Round to 1 decimal place. d) If a person starts in state S what is the expected number of transition before they are absorbed? Round to 1 decimal place.

The transition matrix for an absorbing Markov chain is shown below. PQRS r0.1 0 0 0.21 0.3 1 0 0.2 R 0.1 0 1 0.2 Lo.5 0 0 0.4 a) Rewrite this transition matrix in standard form. b) Find the fundamental matrix, F c) If a person starts in state P, on average, how many transitions will they remain in state P? Round to 1 decimal place. d) If a person starts in state S what is the expected number of transition before they are absorbed? Round to 1 decimal place.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Let G be the graph below. E D B C (a) Construct the transition matrix for a random walk around G.

A: The given graph G is as follows The transition matrix P is a representation of a random walk. P…

Q: Find the steady-state vector for the transition matrix. X = 0 1 0 000 Need Help? 1 8 1 0 1/1/00 Read…

Q: If Joe is in C now, find the probability that he will be in A two weeks late

A: It is an important part of statistics. It is widely used.

Q: A Markov chain is described by the transition diagram 1/4 1/4 S 1/2 1/2 S SA 1/2 1/2 |1/3 1/2 S) Ss…

Q: Find the steady-state vector for the transition matrix. 1/5, 2/5 4/5, 3/5 X =

A: Given a transition matrix 15254535. We have to find the steady-state vector for this matrix.

Q: A Markov chain is described by the transition diagram 1/4 1/4 S 1/2 1/2 SA 1/2 1/2 1/3 1/2 (S) Ss 1…

A: For the given , markov chain, we need to find the probability that the process enters S₂ for the…

Q: At a particular two-year college, a student has a probability of 0.39 of flunking out during a given…

Q: Find the transition matrix from B to B′.B = {(1, 1, 1), (1, 1, 0), (1, 0, 0)}, B′ = {(1, 2, 3), (0,…

Q: Consider the transition matrix 0.7 0.3 0.1 P=0.2 1 10 0.3 0.1 25 45 Find the steady state vector: 18…

A: The steady state vector is x=⎣⎢⎡316121⎦⎥⎤Explanation:

Q: 4. Suppose a Markov chain has transition matrix 1 0.4 0.6 0.3 0.1 0.6 0 0 1 a. Determine R¡ for all…

A: We are given the transition probability matrix of a Markov chain. The hitting probability,…

Q: The transition matrix for a Markov chain is shown to the right. Find Pk for k=2, 4, and 8. Can you…

Q: Part II: Consider a following absorbing Markov chain. 1 0.05 0.95 0.27 0.73 1 Find the matrices A…

A: Given:

Q: Consider the migration (Markov) matrix A = 0.7 0 0.2 0.1 0.4 0.2 [0.2 0.6 0.6 Suppose that,…

A: Given the migration (Markov) matrix, A=0.700.20.10.40.20.20.60.6 Initially, there are 91 residents…

Q: Assume that all bonds in a portfolio can be assigned to three credit ratings: an AAA grade, a BBB…

A: Given:-

Q: Find the steady-state vector for the transition matrix. 3 1 5 5 2 4 5 X =

Q: # 5. The transition matrix for a three-state Markov chain with S = {1,2,3} is P = 0 0 0 0 1 0.5 0.5…

Q: state 1[.1 1 8 1. Consider the transition matrix P= state 25 5 0 state 3.7 0 3 a. Identify what the…

Q: Use a software program or a graphing utility to find the transition matrix from B to B′.B = {(3, 2,…

A: The given bases are,B = {(3, 2, 1), (1, 1, 2), (1, 2, 0)},B′ = {(1, 1, −1), (0, 1, 2), (−1, 4,…

Q: Use a software program or a graphing utility to find the transition matrix from B to B′.B = { (1, 0,…

A: The given bases,One has to find the transition matrix using the graphing utility.

Q: 3. The transition matrix of a chain is >= Find lim Pn for nm P [1-a a В 1 - 3

A: Given information

Q: Find the next 3 states of the initial state 0.1 using the transition matrices lo.6] [0.4 0.0 0.3]…

A: Given information: In the given Markov model, there are 3 states. A state transition matrix consists…

Q: det R have the inner Euclidian fipace product 4=(5,-1) and let X= L1,1) and Find l lyll and Kxy>…

A: Given that x=(1,1) and y=(5,-1)

Q: Consider the transition matrix for a regular Markov chain below. If the process continu for a large…

A: If the process continues for a large number of steps in Markov chain then it reaches to the…

Q: Consider a Markov process with state space S= {1,2,3} and transition matrix P. p= p q…

A: In Markov process having transition matrix ,the Sum of probabilities in each row is 1.This kind of…

Q: Draw a transition diagram that corresponds to the following Markov chain: .98 .80 .95 | a, .02 0. by…

A: From the given information, there are three states: ak, bk, ck. And the transition matrix is,

Q: Could the given matrix be the transition matrix of a regular Markov chain? 0.4 0.6 1 0 Choose the…

A: Transition matrix (stochastic matrix): a matrix that describes transitions and the row sum and…

Q: A Markov chain has the transition probability matrix [0.3 0.2 0.5 0.5 0.1 0.4 0.5 0.2 0.3 What is Pr…

A: A Markov process whose state space is discrete then it is called as Markov chain. Suppose,…

Q: Question 4 0. 23 0.45 a If P = | 0.45 0.13 0.42 | is a transition matrix of a Markov chain, 0. 66…

A: As per our guidelines we can solve first MCQ and rest can be reposted. Solution-: Q.4 Ans: We find…

Q: Which of the transition matrices are regular? Select all that apply: A = 0.5 E = 0.5 0.6 0.4] 03 0.7…

Q: Let (Xn)nzo be a Markov chain with state space S = {A, B, C} and transition matrix P given by |||…

Q: 1 (d) Last week, Amy walked a median of 7.5 kilometres each day. 1 kilometre = 0.6 miles The table…

Question

The transition matrix for an absorbing Markov chain is shown below.
P Q RS
r0.1 0 0 0.21
0.3 1 0 0.2
R
0.1 0 1 0.2
Lo.5 o 0 0.4
a) Rewrite this transition matrix in standard form.
b) Find the fundamental matrix, F
c) If a person starts in state P, on average, how many transitions will they
remain in state P? Round to 1 decimal place.
d) If a person starts in state S what is the expected number of transition
before they are absorbed? Round to 1 decimal place.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Markov Processes and Markov chain$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

A Markov chain has the transition probability matrix 0 1 0 || 0.4 0.4 0.2|| P = 1 ||0.6 0.2 0.2| 2 ll0.4 0.2 0.4| 2. Examples 215 After a long period of time, you observe the chain and see that it is in state 1. What is the conditional probability that the previous state was state 2? That is, find lim Pr{X,-, = 2X, = 1}. 2.
Approximate the stationary matrix S for the transition matrix P by computing powers of the transition matrix P. 0.38 0.62 0.23 0.77 P= S= (Type an integer or decimal for each matrix element. Round to four decimal places as needed.)
Suppose that a Markov chain has the following transition matrix a, az az as a s 3 000 The recurrent states are a 4 4 a₂000 P=a₂00 0 0 a003 as 1 0 0 0
DO NOT COPY OTHER SOLUTIONS. USE A TRANSITION PROBABILITY MATRIX WHEN SOLVING. Consider the following Markov chain. Assuming that the process starts in state 4, what is the probability that we eventually reach the recurrent class {1,2}?
Consider the migration (Markov) matrix A = 0.7 0 0.2 0.1 0.4 0.2 0.2 0.6 0.6 Suppose that, initially, there are 96 residents in location 1, 82 residents in location 2, and 151 residents in location 3. Assume time is measured in years. Find the population in each location after 1 year. Find the population in each location after 2 years.
Which of the following transition matrices is/are for a regular Markov Chain? 0 % 2 0 2 *0 1 1/2 X = % 0 1/2 0. Z = %3D %3D 1/2 2 0 % (A) X,Y, Z (B) Z (C) Х (D) X, Y (E) X, Z (F) none (G) Y (H) Y, Z O A OC OE O F D.
Markov model: d = 33% (success) f = 19% (non-success) 1. Assuming previous success [1 0], what is the probability of having a successful year? 2. What is the probability of having two successful years?
Employment Employment Last Year This Year Percentage Industry Industry 80 Small Business 10 Self-Employed 10 Small Business Industry 10 Small Business 60 Self-Employed 30 Self-Employed Industry 10 Small Business 80 Self-Employed 10 Assume that state 1 is Industry, that state 2 is Small Business, and that state 3 is Self-Employed. Find the transition matrix for this Markov process. P =
Approximate the stationary matrix S for the transition matrix P by computing powers of the transition matrix P. -[: P= 0.33 0.67 0.17 0.83 S= 0 (Type an integer or decimal for each matrix element. Round to four decimal places as needed.)
Pls ans all
Please do not give solution in image format thanku
If he is in C now, find the joint probability that he will be in C in two weeks and in A in four weeks from now