Question no. 10 A machine is made up of two components that operate independently. The lifetime T; (in days) of component i has an exponential distribution with parameter Ai, for i = 1, 2. Suppose that the two components are placed in parallel and that A1 A2 = In 2. When the machine breaks down, the two components are replaced by new ones at the beginning of the following day. Let Xn be the number of components that operate at the end of n days. Then the stochastic pro- cess {Xn,n probability matrix. %3D 0, 1, ...} is a Markov chain. Calculate its one-step transition

Question no. 10 A machine is made up of two components that operate independently. The lifetime T; (in days) of component i has an exponential distribution with parameter Ai, for i = 1, 2. Suppose that the two components are placed in parallel and that A1 A2 = In 2. When the machine breaks down, the two components are replaced by new ones at the beginning of the following day. Let Xn be the number of components that operate at the end of n days. Then the stochastic pro- cess {Xn,n probability matrix. %3D 0, 1, ...} is a Markov chain. Calculate its one-step transition

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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