0.70.3]0.4 0.60.50.0.50.5 0.1]Lo.4States are 0,1,2,3 respectively.a. Does this Markov chain have a steady state distribution? Explain why?b. Suppose that the process is "in control" if it is in states 0 or I and is "out of control" if it is in states 2 or 3. In the long run, what fiaction of the time is the processout of control?

Answered: Image /qna-images/answer/76526ab7-b27e-4f32-96b2-c40f08718949.jpg

Answered: 0.7 031 0.4 0.6 0.5 0.5 0.5 0.1. lo.4…

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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c. The market share of two companies A and B is 30% and 70% in the current time period. The information obtained in terms of the customer loss and retention is given by the matrix P. [0.3 0.2] P = Lo.7 0.8] i.Determine the transition probability matrix in the 1st and 2nd month. ii.What is the steady state of the two companies?
In each step someone randomly selects precisely one number from sequence {1; 2; 3; 4}. The chosen number can be selected again in any of the subsequent steps. The current state of the Markov chain is the minimum of all the numbers selected up to and including the current step. 1. Write the initial distribution and the transition probability matrix for the Markov chain; 2. Draw the graph of the Markov chain; 3. Calculate the probability that after 2 steps the system will be in a state with a number greater than 2.
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 Markov chain specified by the following transition diagram. a. Find the steady-state probabilities of all states. 0.4 b. If the initial state is 7, what is the expected 0.3 0.4 0.2 number of steps to reach state 1 or 3? 0.8 0.2 c. If at step 0 the system was in state 4, what is the probability that after step 3 it was in state 3 and after step 47 it was in state 3 again?
Question 1.16.2 (Markov chains, Part IB, 1991, 307D) Three girls A, B and C are playing table tennis. In each game, two of the girls play against each other and the third girl does not play. The winner of any given game n plays again in game n + 1. The probability that girl x will beat girl y in any game that they play against each other is sx/(Sx+Sy) for x, y = {A,B,C}, x‡y, where sa, SB, SC represent the playing strengths of the three girls. In what proportion of games does each girl play, in the long run?
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.
4. Find the stationary distribution of the Markov chain shown below using the reversible property. OFE 1/2 I 2 1/2 1/4 5/12 3 1/3 1/6 7/12 4 1/4 1/8 7/8 5
Answer all three subparts
3. A discrete Markov model has state space equal to E {0, 1, 2}. The transition probabilities p are independent of r and recorded in the matrix P defined below. .7 .2 .1 P = .1 .6 .3 1 Assume that Lynn is in state 0 at time 0, and that i = .04. (a.) Determine the probability that Lynn is in state 0 at time 3. (b.) Determine the probability that Lynn transitions from state 1 at time 3 to state 2 at time 4.
i need the answer quickly
Given the transition matrix of a Markov process, what is the probability of going to state 3 from state 1 after 3 steps?
Shakira's concerts behave like a Markov chain. If the current concert gets cancelled, then there is an 90% chance that the next concert will be cancelled also. However, if the current concert does not get cancelled, then there is only a 50% chance that the next concert will be cancelled. What is the long-run probability that a concert will not be cancelled? a. 1/4 b. 1/10 c. 1/6 d. 1/2 e. 5/6 f. None of the others are correct

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