1. Given the following (one-step) transition matrices of a Markov chain (MC), draw the state transitiondiagram for each MC, determine the classes of the MC and, for each class determine whether it isrecurrent or transient.(a) P||W|33|13IH43I4LILI310 0 00 0 013300 00000 035|14|W1434(b) P =0000100NITOATTOO O0OLO OLONIMOOOO20 1 0 0 000 130 00OOMITOLIN00034HIMOO3200 0(c) P =OLIM0-3SI51200O12081130WITTHTAGE10250

We have to draw the state transition diagram for each Markov Chain, determine the classes and…

Answered: 1. Given the following (one-step)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Consider a Markov chain (Xn) with state space S = {1, 2, 3, 4, 5} and transition matrix 0.5 0.5 0 0 0 0.4 0.6 0 0 0 P = 0 0.3 0.3 0.4 0 0 0 0 0.6 0.4 000 0.6 0.4 One stationary distribution for this Markov chain is (4, 5, 0, 0, 0). Suppose the Markov chain (X) is started from the initial distribution λ = (0.1 0 0.7 0.2 0). What are the limiting probabilities limn→∞ P(X = i) for each i € S?
Q: Consider the Markov chain defined on states S = {0, 1, 2, 3} whose transition probabilitymatrix is P : ( 1 0 0 0 0.2 0.3 0.1 0.4 0.3 0.1 0.5 0.1 0 0 0 1 ) It is known that the process starts in state 1.(a) Determine the probability that the Markov chain ends in state 0.(b) Determine the mean time that the process spends in state 1 prior to absorption.(c) Determine the mean time that the process spends in state 2 prior to absorption.(d) Determine the mean time to absorption.
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.
Let {X(t);t≥0} be a Continuous Time Markov chain with state space S={1,2} . The process is such that after an exponential random time with parameter λ=1 , it moves from state 1 to state 2, and then remains at state 2. (a) The entries of the generator matrix Q are q11 Answer q12 Answer q21 Answer q22 Answer (b) Based on results for part (a); the transition probability matrix P(3) (i.e at time t=3 ) is (round off probabilty to two decimal points) p11 Answer p12 Answer p21 Answer p22 Answer
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 =
Recall that the graph of a discrete-time, finite-state, homogeneous Markov chain on two states 1, 2 with transition matrix is CO (: :) 1 T = If instead a new Markov chain on three states {1, 2, 3} has transition matrix 10 1 0 (a) Draw the corresponding graph for this new Markov chain. (b) Is the Markov chain with transition matrix T irreducible?
1. For each of the transition matrices given below, list absorbing state(s), and determine the period of each of the states in each Markov chain. (a) P = (d) P = 1120 CLI2L 1434L3 0 ܚ . ܟ ܝ. | ܟ ܝܕ . ܚ 0 00 0 0 0 0 0 3I4LI4 LIABI+ 0 0 (b) P = 1 0 Lo (e) P = 0 1 1 0 0 1333 COLITOLIN 0 0 0 0 0 213 100 0 0 3 00 100 0 -0 WIN 1 0 0 0 0 0 0 00 1 0 0 4|012 TWO O 0 0 0 0 0 (c) P = (f) P = 0 1|2 1|3 OLT20IN +15 O N|TN|TO 120 HINO OLI3 O 0 LI5L4L 1113 2I5
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

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