2. (a) Write down the one-step transition matrix P for the following state transition diagram.(b) Find the n-step transition matrix P(¹) for n = 200 and 300. Then determine if this Markov chain hassteady-state?0.4200.50.2(4)0.30.60.810.23

Answered: (a) Write down the one-step transition…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Safari File Edit View History Bookmarks Window Help Wed 10:51 A myopenmath.com Netflix МyOpenMath b My Questions | bartleby You are conducting a study to see if the accuracy rate for fingerprint identification is significantly different from 0.75. Your sample data produce the test statistic z = places. - 2.71. Find the p-value accurate to 4 decimal Submit Question
Problem 2. Tlaloc has 4 umbrellas, each either t home or at work. Each time he goes to work or back, it rains with probability p, independently of all other times. If it rains and there is at least one umbrella with him, he takes it. Otherwise, he gets wet. Let Xn be the number of umbrellas at his current location after n trips (so n even corresponds to home and n odd to work. (a) Find the transition probabilities for the Markov chain Xn. (b) Show that it is reversible and find the stationary distribution. (c) What is the probability that Tlaloc gets wet on any given trip? (d) What value of p maximizes this probability? (e) What happens if he has N umbrellas for N other than 4?
Determine whether the statement below is true or false. Justify the answer. If (x) is a Markov chain, then X₁+1 must depend only on the transition matrix and xn- Choose the correct answer below. O A. The statement is false because x, depends on X₁+1 and the transition matrix. B. The statement is true because it is part of the definition of a Markov chain. C. The statement is false because X₁ +1 can also depend on X-1 D. The statement is false because X₁ + 1 can also depend on any previous entry in the chain.
C)
3. (a) A Markov process with 2 states is used to model the weather in a certain town. State 1 corresponds to a suny day. State 2 corresponds to a rainy day. The transition matrix for this Markov process is [0.7 0.4] 0.3 0.6 %3D (i) If today is rainy, what is the probability that tomorrow will be sunny? (ii) Find the steady state probability vector. (iii) In the long run, how many days a week are sunny?
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
Linear Algebra
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
plz solve only (ii) part...

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(a) Write down the one-step transition matrix P for the following state transition diagram. (b) Find the n-step transition matrix P(n) for n = 200 and 300. Then determine if this Markov chain has steady-state? (4)