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.A certain type component has two states: 0 = off and 1 = operating. In state 0, the process remains in the state an exponential amount of time with rate o, and then moves to state 1. The component spends an exponential amount of time with rate 3 in state 1 after which the process returns to state 0. A system consists of two such components A and B. Assume the amounts of time the components spend in the states are independent of one another and have rates given by the following. Component Off Rate (a) Operating Rate (3) 4 A 2 B 3 6 Consider the continuous-time Markov chain with states {0,4,B,2} representing the component currently operating. Enumerate the transition rates v; and the transition probabilities pij of the Markov chain.

.A certain type component has two states: 0 = off and 1 = operating. In state 0, the process remains in the state an exponential amount of time with rate o, and then moves to state 1. The component spends an exponential amount of time with rate 3 in state 1 after which the process returns to state 0. A system consists of two such components A and B. Assume the amounts of time the components spend in the states are independent of one another and have rates given by the following. Component Off Rate (a) Operating Rate (3) 4 A 2 B 3 6 Consider the continuous-time Markov chain with states {0,4,B,2} representing the component currently operating. Enumerate the transition rates v; and the transition probabilities pij of the Markov chain.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 65EQ
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.A certain type component has two states: 0 = off and 1 = operating. In state 0, the process remains in the state an exponential amount of time with rate o, and then moves to state 1. The component spends an exponential amount of time with rate 3 in state 1 after which the process returns to state 0. A system consists of two such components A and B. Assume the amounts of time the components spend in the states are independent of one another and have rates given by the following. Component Off Rate (a) Operating Rate (8) 4 A 2 B 3 6 Consider the continuous-time Markov chain with states {0,4,B,2} representing the component currently operating. Enumerate the transition rates v; and the transition probabilities pij of the Markov chain.
Transcribed Image Text:.A certain type component has two states: 0 = off and 1 = operating. In state 0, the process remains in the state an exponential amount of time with rate o, and then moves to state 1. The component spends an exponential amount of time with rate 3 in state 1 after which the process returns to state 0. A system consists of two such components A and B. Assume the amounts of time the components spend in the states are independent of one another and have rates given by the following. Component Off Rate (a) Operating Rate (8) 4 A 2 B 3 6 Consider the continuous-time Markov chain with states {0,4,B,2} representing the component currently operating. Enumerate the transition rates v; and the transition probabilities pij of the Markov chain.
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