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Let {Xn, n = 0, 1, 2, . . .} be a three-state Markov chain with S = {0, 1, 2} and the transition probability matrix Г0.1 0.3 0.67 P = 0.7 0.3 0 0.5 0 0.5 State 0 represents an operating state of some system, while states 1 and 2 represent repair states (corresponding to two types of failures). We assume that the process begins in state ✗0 = 0, and then the successive returns to state 0 from the repair state form a renewal process. Determine the mean duration of one of these renewal intervals. E[renewal interval]: =

Let {Xn, n = 0, 1, 2, . . .} be a three-state Markov chain with S = {0, 1, 2} and the transition probability matrix Г0.1 0.3 0.67 P = 0.7 0.3 0 0.5 0 0.5 State 0 represents an operating state of some system, while states 1 and 2 represent repair states (corresponding to two types of failures). We assume that the process begins in state ✗0 = 0, and then the successive returns to state 0 from the repair state form a renewal process. Determine the mean duration of one of these renewal intervals. E[renewal interval]: =

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 55E
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Let {Xn, n = 0, 1, 2, . . .} be a three-state Markov chain with S = {0, 1, 2} and the transition probability matrix [0.1 0.3 0.6] P = 0.7 0.3 0 [0.5 0 0.5 State O represents an operating state of some system, while states 1 and 2 represent repair states (corresponding to two types of failures). We assume that the process begins in state ✗( = 0, and then the successive returns to state 0 from the repair state form a renewal process. Determine the mean duration of one of these renewal intervals. E[renewal interval] = =
Transcribed Image Text:Let {Xn, n = 0, 1, 2, . . .} be a three-state Markov chain with S = {0, 1, 2} and the transition probability matrix [0.1 0.3 0.6] P = 0.7 0.3 0 [0.5 0 0.5 State O represents an operating state of some system, while states 1 and 2 represent repair states (corresponding to two types of failures). We assume that the process begins in state ✗( = 0, and then the successive returns to state 0 from the repair state form a renewal process. Determine the mean duration of one of these renewal intervals. E[renewal interval] = =
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