For the attached transition probability matrix for a Markov chain.(a) Compute P{X2 = 3|X0 = 1}.(b) Compute P{X6 = 3|X4 = 1, X3 = 2}. 1 2310.20.3 0.5P = 23 \ 0.10.4 0.40.20.2 0.7/

Solution: From the given information, the transition probability matrix for a Markov chain is

Answered: 1 2 3 1 0.2 0.3 0.5 P = 2 0.4 0.4 0.2 3…

Math

Probability

1 2 3 1 0.2 0.3 0.5 P = 2 0.4 0.4 0.2 3 0.1 0.2 0.7

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

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...

See similar textbooks

Related questions

Q: ou have a markov chain and you can assume that P(X0 = 1) = P(X0 = 2) = 1/2 and that the matrix looks…

A: P(X0 = 1) = P(X0 = 2) = 12 P=12121323

Q: 2. Let Xo, X₁,... be the Markov chain on state space {1,2,3,4} with transition matrix 1/2 1/2 0 0…

A: Given that be the Markov chain on state space with transition matrix:

Q: (1) If volume is high this week, then next week it will be high with a probability of 0.6 and low…

A: Assume that state 1 is high volume and state 2 is low volume. 1) Given that, if the volume is high…

Q: Suppose that X k is a time-homogenous Markov chain. Show thatP{X3= j3, X2= j2|X0= j0,X1 = j1}= P{X3…

A: The objective of the question is to prove the Markov property for a time-homogenous Markov chain.…

Q: Let X be a random variable with sample space {1,2,3} and probability distribu- tion (). Find a…

A: The x is random variable with sample space { 1, 2, 3}Know that,

Q: If you eat Kebsah today, there is a probability of 1/5 that you will eat it tomorrow. If you do not…

A: Let's define two states:State 0 (Non-Kebsah): This state represents the situation when Kebsah is not…

Q: A Markov chain Xo, X₁, X₂... on states 0, 1, 2 has the transition probability matrix P (shown on the…

A: Given a Markov chain with three states 0, 1 and 2. Also, the transition probability matrix is…

Q: P is the transition matrix of a regular Markov chain. Find th e long range transition matrix L of P

Q: [4/5 1/5] [3/5 2/5 A regular Markov chain has transition matrix P = What is the first entry of…

A: Let X is the stable vector such that X=[a b] Now, XP=X[a b]45153525=[a b]4a5+3b5=aa5+2b5=b when we…

Q: Prove that the square of a Markov matrix is also a Markov matrix.

A: An n×n matrix is called Markov matrix if all entries are non negative and the sum of each column…

Q: Find the vector of stable probabilities for the Markov chain whose transition matrix is [0.4 0.6 1 1…

A: The answer is given as follows :

Q: 15. For which of the following transition matrices are the corresponding markov chains regul [1/2…

A: Consider the given matrices: X1=12120001100 , X2=00100112120 and X3=121210

Q: Find the vector of stable probabilities for the Markov chain with this transition matrix. 1 P =

Q: ) If volume is high this week, then next week it will be high with a probability of 0.6 and low with…

A: Given information that Volume is high, the next week it will be high probability 0.6 and low…

Q: Find the vector of stable probabilities for the Markov chain whose transition matrix is 1 1 0.2 0.8…

A: In question, Given the Markov chain with transition matrix. Then we'll find the stable probability…

Q: A cellphone provider classifies its customers as low users (less than 400 minutes per month) or high…

A: Given data: 40% of people who were low users 30% of the people who were high users

Q: A Markov Chain has the transition matrix P = 1 and currently has state vector % % |. What is the…

A: From the given information, P=121201Let π=1656 Consider, the probability vector at stage 1 is,…

Q: Find the vector of stable probabilities for the Markov chain whose transition matrix is

A: Let the stable vector of probabilities be; W=xyzwhere;x+y+z=1 Let; P=01000.60.4100

Q: 1/4 3/4 3/4 2 1/4 Figure 3.10 A two-state discrete Markov chain . Consider the discrete-time Markov…

Q: 15. For which of the following transition matrices are the corresponding markov chains regul [1/2…

A: NOTE:- We know that a markov chain transition matrix M will be regular when for some power of M…

Q: Determine whether the Markov chain with matrix of transition probabilities P is absorbing. Explain.

Question

For the attached transition probability matrix for a Markov chain.

(a) Compute P{X₂ = 3|X₀ = 1}.
(b) Compute P{X₆ = 3|X₄ = 1, X₃ = 2}.

1 2
3
1
0.2
0.3 0.5
P = 2
3 \ 0.1
0.4 0.4
0.2
0.2 0.7/

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Markov Processes and Markov chain$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

A Markov chain has the transition matrix shown below: [0.4 0.3 0.3] P=0.8 0.2 0 00 1 (Note: Express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) (1) Find the two-step transition matrix P(2) = [ (2) Find the three-step transition matrix P(3) = (3) Find the three-step transition probability p32(3) =
Find the steady state matrix X of the absorbing Markov chain with matrix of transition probabilities P. 0.4 0 0.3 1 0.6 0 0.1 X = P = 0.3 0.3 000
(i) If volume is high this week, then next week it will be high with a probability of 0.6 and low with a probability of 0.4. (ii) If volume is low this week then it will be high next week with a probability of 0.1. Assume that state 1 is high volume and that state 2 is low volume (1) Find the transition matrix for this Markov process. (2) If the volume this week is high, what is the probability that the volume will be high two weeks from now? (3) What is the probability that volume will be high for three consecutive weeks?
a)
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)
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
Find the vector of stable probabilities for the Markov chain whose transition matrix is