# HW8 - IE 336 Mar 28 2011 Handout#9 Due Apr 4 2011 Homework...

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IE 336 Handout #9 Mar. 28, 2011 Due Apr. 4, 2011 Homework Set #8 1. Let the following function represent a realization of a continuous time Markov process during a time span of 31 hours. Assume that the process has only 2 states. t (hours) 12 2 9 22 19 16 7 29 31 25 27 3 1 state (a) Estimate the transition rates of the process. (b) Form the system of diﬀerential equations that as a solution has the transition proba- bilities as functions of time. (Do not solve the system.) (c) If the process is in state 2 what is the expected length of time that it will stay in state 2 before a transition to state 1 occurs. (d) If the process has been in state 1 for 10 minutes what is the expected length of time that it will stay in state 1 before a transition to state 2 occurs. 2. Consider a continuous time Markov process with the following transition rate matrix. Λ = - 5 2 q p 2 r - 3 2 p 4 r q - 4 . (The transition rates given in the above matrix are in number of transitions per one hour.)

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## This note was uploaded on 01/19/2012 for the course IE 230 taught by Professor Xangi during the Spring '08 term at Purdue.

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HW8 - IE 336 Mar 28 2011 Handout#9 Due Apr 4 2011 Homework...

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