Chapter 17 Part 2 - Agenda for Next Week Friday April 8 No...

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Unformatted text preview: Agenda for Next Week Friday, April 8 No Class (use class time to work on Case 2) Monday April 11 Case 2 due Markov Processes Wednesday, April 13 Markov Processes (HWs) Final Project Topic Due Friday, April 15 Case 3 Review Dynamic Programming Chapter 17 Markov Processes – Part 2 Review • A Markov Process describes a situation where a system is in one state at a time • Switching between states is probabilistic • The state of the system is dependent ONLY on the previous state of the system Example: Machine Adjustment To To From From In adj. (1) In adj. (1) Out of adj. (2) Out of adj. (2) In In adjustment adjustment (state 1) (state 1) 0.7 0.7 0.6 0.6 Out of Out of adjustment adjustment (state 2) (state 2) 0.3 0.3 0.4 0.4 Example: Machine Adjustment Day 1 1 1 2 2 1 1 .7 .7 .3 .3 Day 2 .7 .7 .3 .3 If the machine is found to be in adjustment on day 1, what is the likelihood it will be in adjustment on day 3? Not in adjustment? Example: Machine Adjustment 1 1 2 2 1 1 2 2 1 1 2 2 1 1 .7 .7 .3 .3 .7 .7 .3 .3 .6 .6 .4 .4 .49 .49 .21 .21 .18 .18 .12 .12 Day 1 Day 2 .67 .67 .33 .33 Day 3 1 1 2 2 1 1 2 2 1 1 2 2 1 1 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 .7 .7 .3 .3 .7 .7 .3 .3 .6 .6 .4 .4 .7 .7 .3 .3 .7 .7 .3 .3 .6 .6 .4 .4 .6 .6 .4 .4 Day 4 1 1 2 2 1 1 2 2 1 1 2 2 1 1 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 .7 .7 .3 .3 .7 .7 .3 .3 .6 .6 .4 .4 .7 .7 .3 .3 .7 .7 .3 .3 .6 .6 .4 .4 .6 .6 .4 .4 Day 4 Example: Machine Adjustment Day 4: P(S1|S1) = .7(.7)(.7) + .7(.3)(.6) +.3(.6)(.7) +.3(.4)(.6) = .667 P(S2|S1) = .7(.7)(.3) + .7(.3)(.4) + .3(.6)(.3) + 3(.4)(.4) = .333 Day 5...
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Chapter 17 Part 2 - Agenda for Next Week Friday April 8 No...

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