If the student attends class on a certain Friday, then he is four times as likely to be absent the next Friday as to attend. If the student is absent on a certain Friday, then he is five times as likely to attend class the next Friday as to be absent again. Assume that state 1 is Attends Class and that state 2 is Absent from Class. Find the transition matrix for this Markov process. P =

If the student attends class on a certain Friday, then he is four times as likely to be absent the next Friday as to attend. If the student is absent on a certain Friday, then he is five times as likely to attend class the next Friday as to be absent again. Assume that state 1 is Attends Class and that state 2 is Absent from Class. Find the transition matrix for this Markov process. P =

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

Similar questions

Please help me answer this. Thank you.
Suppose that a Markov chain has the following transition matrix The recurrent states are a A₁ A₂ A3 A4 A5 0 0 0 a₂000 P=a, 0 0 1 0 0 2 a 0 0 0 as 10000
Problem: Construct an example of a Markov chain that has a finite number of states and is not recurrent. Is your example that of a transient chain?
We will use Markov chain to model weather XYZ city. According to the city’s meteorologist, every day in XYZ is either sunny, cloudy or rainy. The meteorologist have informed us that the city never has two consecutive sunny days. If it is sunny one day, then it is equally likely to be either cloudy or rainy the next day. If it is rainy or cloudy one day, then there is one chance in two that it will be the same the next possibilities. In the long run, what proportion of days are cloudy, sunny and rainy? Show the transition matrix.
If A is a Markov matrix, why doesn't I+ A+ A2 + · · · add up to (I -A)-1?
A Markov system with two states satisfies the following rule. If you are in state 1 then of the time you change to state 2. If you are in state 2 then of the time you remain in state 2. state 1 Write the transition matrix for this system using the state vector v state 2 T = Find the long term probability (stable state vector). vs
A Markov chain has two states. • If the chain is in state 1 on a given observation, then it is three times as likely to be in state 1 as to be in state 2 on the next observation. If the chain is in state 2 on a given observation, then it is twice as likely to be in state 1 as to be in state 2 on the next observation. Which of the following represents the correct transition matrix for this Markov chain? О [3/4 2/3 1/4 1/3 O [2/3 1/3 3/4 1/4) о [3/4 2/3 1/3] None of the others are correct 3/4 O [1/4 1/3 2/3. O [3/4 1/4] 1/3 2/3.
Consider a random walk on the graph with 6 vertices below. Suppose that 0 and 5 are absorbing vertices, but the random walker is more strongly attracted to 5 than to 0. So for each turn, the probability that the walker moves right is 0.7, while the probability he moves left is only 0.3. (a) Write the transition matrix P for this Markov process. (b) Find POO. (c) What is the probability that a walker starting at vertex 1 is absorbed by vertex 0? (d) What is the probability that a walker starting at vertex 1 is absorbed by vertex 5? (e) What is the probability that a walker starting at vertex 4 is absorbed by vertex 5? (f) What is the probability that a walker starting at vertex 3 is absorbed by vertex 5? What is the expected number of times that a walker starting at vertex 1 will visit vertex 2? (h) What is the expected number of times that a walker starting at vertex 1 will visit vertex 4? N;B The diagram is a horizontal line showing points 0, 1, 2, 3, 4, and 5
A state vector X for a four-state Markov chain is such that the system is three times as likely to be in state 4 as in 3, is not in state 2, and is in state 1 with probability 0.2. Find the state vector X.
A Markov system with two states satisfies the following rule. If you are in state 1 then of the time you change to state 2. If you are in state 2 then of the time you remain in state 2. At time t = 0, there are 100 people in state 1 and no people in the other state. state 1 Write the transition matrix for this system using the state vector v = state 2 T = Write the state vector for time t = 0. Vo Compute the state vectors for time t = 1 and t = 2. Vị = V2
At Suburban Community College, 30% of all business majors switched to another major the next semester, while the remaining 70% continued as business majors. Of all non-business majors, 10% switched to a business major the following semester, while the rest did not. Set up these data as a Markov transition matrix. HINT [See Example 1.] (Let 1 business majors, and 2 = non-business majors.) = Calculate the probability that a business major will no longer be a business major in two semesters' time.
A Markov chain model for a species has four states: State 0 (Lower Risk), State 1 (Vulnerable), State 2 (Threatened), and State 3 (Extinct). For t 2 0, you are given that: 01 zit = 0.03 12 t= 0.05 23 Hit = 0.06 This species is currently in state 0. Calculate the probability this species will be in state 2 ten years later. Assume that reentry is not possible. (Note: This question is similar to #46.2 but with constant forces of mortality) Possīble Answers A 0.02 0.03 0.04 D 0.05 E 0.06