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

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

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: |A B A Markov chain has transition matrix P = [c 1/3 Thus (for example), p12 = B. The state space is…

A: Given a Markov chain has transition matrix, P=ABC13 The average number of visits to state 1 between…

Q: (a) Calculate the matrix P(2) (in terms of the constants a and b). (b) If the probability of the…

Q: Let (X0, X1, X2, . . .) be the discrete-time, homogeneous Markov chain on state space S = {1, 2, 3,…

A: Let be the discrete-time, homogeneous.Markov chain on state space with and transition matrix

Q: 1. A Markov chain with state space S = {1, 2, 3} has transition matrix P = O HINO 0 1 1 OHINO (a)…

A: Given a Markov chain with state space has transition matrix:

Q: Let (X: n 0, 1, 2, ...} be a Markov chain with two states 1, 2 with the following one-step…

A: There are two states 1, 2 P(state 1 to state 1) in one step = 1/4 P(state 1 to state 2) in one step…

Q: If a Markov chain starts in state 2, the probability that it is still in state 2 after THREE…

A: 1) True, p223 is thr probability that the Markov chain remains in state 2 after 3 transitions. 2)…

Q: matrix for the Markov chain that models this situation. 3 1/4 1/4 1/2 0 1/3 2/3 0 robots at each…

A: The possible transition paths of robots are given as:

Q: Please do the questions with handwritten working. I'm struggling to understand what to write

Q: suppose a continuous time markov process with three states s = {1, 2, 3} and suppose the transition…

Q: Consider the Markov chain having a three state space, namely (EO, E1, E2) and transition matrix P, P…

A: The Markov chain has state space: The transition matrix:The initial probabilities:The probability…

Q: A machine is running continuously except when it is broken. Suppose that while the machine is…

Q: Profits at a securities firm are determined by the volume of securities sold, and this volume…

A: 1.Given, If the volume of securities sold is high this week, then the probability that it will be…

Q: Let X, be a continuous-time Markov chain with state space {1, 2} and rates a(1, 2) = 1, a(2, 1) = 4.…

A: For a continuous-time Markov chain, a transition rate matrix is defined as G=gij: i,j∈S, where S is…

Q: Suppose that a Markov chain with 4 states and with transition ma on the fifth observation. Which of…

A: Given that

Q: Suppose a math professor collects data on the probability that students attending a given class…

Q: Čonsider a 4-state Markov chain (X, : t = 0, 1, 2, 3, ..) with state space S = (1, 2, 3, 4) and…

A: The Markov chain is the process X1, X2, ..., Xn The basic property of a Markov chain is that only…

Q: Please do question 1b, 1c and 1d with full working out. I'm struggling to understand what to write

A: The solution of the question is given below:

Q: Consider the Markov chain X given by the diagram 0 10 1 12 2 FO 2 a) Write down the (1-step)…

Q: 5A An ion channel can be in either open or closed state. If it is open, then it has probability 0.1…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 00 (Note: Express your answers as decimal fractions rounded to 4 decimal places (if they have more…

A: Given: The given matrix is as follows, P=0.40.10.50.30.70⊥00

Q: T= 00 3 w|wo|wo|TOO 3 1|21|20 H2H2OOO 1|21|200 00 00 0 0 Hint: Be sure to state your ordering of the…

A: In the given question, we are asked to show that the eigenvalue λ=1 is an eigenvalue of the matrix…

Q: 2. Consider a Markov chain X = (Xn)n20 with state space S = {1, 2, 3} and transition matrix [0.5 0…

A: First, let's recall what transient and recurrent states are:Transient state: A state is called…

Q: Consider a continuous-time Markov chain with transition rate matrix 0. 2 3 Q 1 0 3 1 2 0 What are…

A: Given a continuous-time Markov chain with transition rate matrix Q=023103120

Q: A generator for a continuous time Markov process X(t) is given by G = 2 2 ー人 (1 0 a

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: An Uber driver operates in three parts of a city: A, B, C. Suppose that you keep track of their…

A: As per policy the answer of first three subparts are provided. The given transition matrix is…

Q: 3. A fair die is thrown repeatedly and independently. The process is said to be in state j at time n…

Q: 1. An intensity matrix of a continuous-time homogeneous Markov chain X is given by -4 ... Q 0 ... 1…

A: (a) Completing the Intensity Matrix Q and Drawing the Transition DiagramCompleting the matrix Q:We…

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: Consider a continuous-time Markov chain with transition rate matrix 0 2 3 Q-10 3 1 2 0, What are the…

Q: Suppose that a Markov chain with 4 states and with transition matrix P is in state 4 on the fourth…

A: Given that

Q: A The transition matrix for a Markov chain is shown to the right. B (A) If So=[01], find S₂, S4, Sg.…

A: We have to find S2, S4, S8. According to our guidelines we can solve only 3 subparts so please…

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: Consider a Markov chain with the following state transition matrix and initial probability state…

Question

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

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: Given information:

VIEW

Step 2: Find the entries of the generator matrix Q:

VIEW

Step 3: Calculate the transition probability matrix P(3):

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

A Markov Chain has the transition matrix P 3D 0. 1 and currently has state vector % %% . What is the probability it will be in state 1 after two more stages (observations) of the process? 6. (A) % 3/4 (B) 0 1/12 (D) ½4 (E) 2 /12 1/4 (G) 1 (H) 23/24 O A O B OD O E OF OG H.
Can someone please help me with this question. I am having so much trouble.
Please help me answer this. Thank you.
Consider a time-homogeneous markov chain (Xt: t = 0,1, 2, ...) with states (1,2,3}. what is P[X1 a, X4 = d | XO = i0]?
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) =
an 15 A continuous-time Markov chain (CTMC) has three states (1, 2, 3). ed dout of The average time the process stays in states 1, 2, and 3 are 3, 11.9, and 3.5 seconds, respectively. question The steady-state probability that this CTMC is in the second state ( , ) is
(6) Give an example of a Markov chain Xn on a countable state space S and a function g on S such that g(Xn) is not a Markov chain. Can you give any conditions on Xn and g which ensure that g(Xn) is a Markov chain?
a)
A Markov system with two states satisfies the following rule. If you are in state 1 then of the time you change to state 2. If you are in state 2 then of the time you remain in state 2. state 1 Write the transition matrix for this system using the state vector v state 2 T = Find the long term probability (stable state vector). vs
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
C)
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