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 a, and then moves to state 1. The component spends an exponential amount of time with rate ß 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 (B) A 4 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 a, and then moves to state 1. The component spends an exponential amount of time with rate ß 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 (B) A 4 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 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...

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