Consider a system with two components [ASH 1970]. We observe the state of thesystem
Chapter 7, Problem 1(choose chapter or problem)
Consider a system with two components [ASH 1970]. We observe the state of thesystem every hour. A given component operating at time n has probability p offailing before the next observation at time n + 1. A component that was in a failedcondition at time n has a probability r of being repaired by time n + 1, indepen-dent of how long the component has been in a failed state. The component failuresand repairs are mutually independent events. Let Xn be the number of compo-nents in operation at time n. {Xn | n = 0, 1,...} is a discrete-time homogeneousMarkov chain with the state space I = {0, 1, 2}. Determine its transition proba-bility matrix P, and draw the state diagram. Obtain the steady-state probabilityvector, if it exists
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