A Markov chain X₁, X₁, X₂ ... on the states 0, 1, 2, 3 hasthe transition probability matrix1 230.5 0 0.40 100 01000P02300.1001a. Show that P is regular.b. Determine the limiting distribution.

To determine if a Markov chain with transition probability matrix P is regular, we need to check if…

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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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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Please do the following question with handwritten working out
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?
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
Q 4
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)
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Suppose that a Markov chain with 3 states and with transition matrix P is in state 3 on the first observation. Which of the following expressions represents the probability that it will be in state 1 on the third observation? (A) the (3, 1) entry of P3 (B) the (1,3) entry of P3 (C) the (3, 1) entry of Pª (D) the (1,3) entry of P2 (E) the (3, 1) entry of P (F) the (1,3) entry of P4 (G) the (3, 1) entry of P2 (H) the (1,3) entry of P
For the attached Markov chain with the following transition probability matrix: The Markov chain has only one recurrent class. Determine the period of this recurrent class.
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
Consider a Markov chain with two possible states, S = {0, 1}. In particular, suppose that the transition matrix is given by Show that pn = 1 P = [¹3 В -x [/³² x] + B x +B[B x] x 1- B] (1-x-B)¹ x +B x -|- -B ·X₁ В
Suppose a Markov Chain has transition matrix % 0 % % If the system starts in state 3, what is the probability that it goes to state 2 on the next observation, and then goes to state 4 on the following observation? (A) 24 (B) 1 (C) 4 (D) ½24 (E) % (F) %32 (G) 0 (H) %

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A Markov chain X₁, X₁, X₂ ... on the states 0, 1, 2, 3 has the transition probability matrix 1 2 0.5 0 0 1 0 0 00 P: = 0 1 2 3 0 0.1 0 0 1 3 0.4 0 1 0