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1. An intensity matrix of a continuous-time homogeneous Markov chain X is given by -4 1 Q = 0 3 0 (a) Complete the matrix Q. Draw the transition diagram of X. (b) Find the average time X spends in each state and the probability of making a jump between states. (c) Let q₁ = -qii. Use the following integrated form of Kolmogorov backward equation to find the transition (probability) matrix [P,]ij = P(X = j\X₁ = i) of X, Pij(t) = Pij(0)eit + k#i ΣΕ -qu e "qik Pkj(t - u)du. (d) Verify your solution for the transition probability pij(t) by checking the limit Q = lim where I is a (3 × 3)-identity matrix. (P,-I) 10 t

1. An intensity matrix of a continuous-time homogeneous Markov chain X is given by -4 1 Q = 0 3 0 (a) Complete the matrix Q. Draw the transition diagram of X. (b) Find the average time X spends in each state and the probability of making a jump between states. (c) Let q₁ = -qii. Use the following integrated form of Kolmogorov backward equation to find the transition (probability) matrix [P,]ij = P(X = j\X₁ = i) of X, Pij(t) = Pij(0)eit + k#i ΣΕ -qu e "qik Pkj(t - u)du. (d) Verify your solution for the transition probability pij(t) by checking the limit Q = lim where I is a (3 × 3)-identity matrix. (P,-I) 10 t

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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1. An intensity matrix of a continuous-time homogeneous Markov chain X is given by -4 1 Q = 0 3 0 (a) Complete the matrix Q. Draw the transition diagram of X. (b) Find the average time X spends in each state and the probability of making a jump between states. (c) Let q₁ = -qii. Use the following integrated form of Kolmogorov backward equation to find the transition (probability) matrix [P,]ij = P(X = j\X₁ = i) of X, Pij(t) = Pij(0)eit + k#i ΣΕ -qu e "qik Pkj(t - u)du. (d) Verify your solution for the transition probability pij(t) by checking the limit Q = lim where I is a (3 × 3)-identity matrix. (P,-I) 10 t
Transcribed Image Text:1. An intensity matrix of a continuous-time homogeneous Markov chain X is given by -4 1 Q = 0 3 0 (a) Complete the matrix Q. Draw the transition diagram of X. (b) Find the average time X spends in each state and the probability of making a jump between states. (c) Let q₁ = -qii. Use the following integrated form of Kolmogorov backward equation to find the transition (probability) matrix [P,]ij = P(X = j\X₁ = i) of X, Pij(t) = Pij(0)eit + k#i ΣΕ -qu e "qik Pkj(t - u)du. (d) Verify your solution for the transition probability pij(t) by checking the limit Q = lim where I is a (3 × 3)-identity matrix. (P,-I) 10 t
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