Let (Xp: n- 0, 1, 2,. ...] be a Markov chain with two states 1, 2 with the following one-step transition probability matrix P.state1/43/41/21/2If Xo = 1, what is the probability that in exactly two steps after starting (i.e., at n -2) the state is 2 for the FIRST TIME?O 1/8O none of the other choicesO 3/16O 1/4

Given that there are two states in a chain 1, 2 Initially the chain is at state 1 i.e., X0 = 1 Also…

Answered: Let (X: n = 0, 1, 2, ..] be a Markov…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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
5. Suppose {Xn, n 2 0} is a Markov chain with state space (0, 1,2} and transition probability matrix 0.6 0.2 0.2 P= 0.8 0.2 0.5 0.5 Find the classes for this Markov chain and classify them as transient or recurrent.
- Consider a Markov chain on {1,2} with the given transition matrix P shown below. Use two methods to find the probability that, in the long run, the chain is in state 1. First, raise P to a high power. Then directly compute the steady-state vector. P= 0.9 0.2 0.1 0.8 Raise P to a high power. For the purposes of this solution, raise P to the 100th power. p100 (Type an integer or decimal for each matrix element. Round to five decimal places as needed.)
A Markov chain {s} with state space n={1, 2, 3} has a sequence of realizations and process transitions as follows: Transition (1,1) (1,2) (1,3) (2,1) (2,2) (2,3) (3.1) (3,2) (3,3) t S: S+1 2 1 1. 1 1 1 1 1 3 1 3 3 3 4 3 1. 2 3 1. 2 1 7 2 2 1. 8 2 2 1 9 2 3 1. 10 3 11 1 1 12 1 1. 13 1 1. 14 1. 1. 15 3 1. 1. 16 1. Number of frequencies : 1 3. 2 2 1 1 1 1 a. determine the transition frequency matrix O= 2 12 93 021 022 °23 %3D 31 °32 °33) 1 P1 P12 P13 b. determine the estimated transition probability matrixP= 2 P21 P22 P23 3 P31 P32 P33)
Pls ans all
2. Let Xo, X₁,... be the Markov chain on state space {1,2,3,4} with transition matrix (1/2 1/2 0 0 1/7 0 3/7 3/7 1/3 1/3 1/3 0 0 2/3 1/6 1/6/ (a) Explain how you can tell this Markov chain has a limiting distribution and how you could compute it.
Given the transition matrix of a Markov process, what is the probability of going to state 3 from state 1 after 3 steps?
Which of the following transition matrices is/are for a regular Markov Chain? 0 0 1 X = % 0 0 0 1 Y =|0 ½ ½ Z = % 0 2 (A) Y (В) X, Y (С) х (D) Y, Z (E) none (F) X, Z (G) (Н) Х, Y, Z
explanation needed for 11)
Consider the Markov chain with three states,S={1,2,3}, that has the following transition matrix 1.Draw the state transition diagram for this chain. (10 marks)
Q3) The state transition matrix of a Markov random process is given by 1/3 1/3 1/6 1/6 5/9 0 0 4/9 2/5 1/5 1/5 1/5 0 0 3/20 17/20 [ ] Draw the state transition diagram and denote all the state transition probabilities on the same. Find P[X1 = 2] List the pairs of communicating states. Find P[X2 = 3| X1 = 2] Compute P[X2 = 2 | X0 = 1] Compute P[X3 = 3, X2 = 1, X1 = 2 | X0 = 3] (vii) Find P[X4 = 4, X3 = 3, X2 = 3, X1 = 1, X0 =2] where Xt denotes the state of the random process at time instant t. The initial probability distribution is given by X0 = [2/5 1/5 1/5 1/5].
1. A Markov chain has state space {0, 1, 2} and transition probability matrix .1 .5 .4 P = 0 0 1 .2 .3 .5 (a) the probability of going from state 0 to state 2 in 2 transitions (b) the steady-state distribution, if it exists Determine:

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