IOE+316+Homework+1

# IOE+316+Homework+1 - (a ⋅ 1 3 2 5 x x =(b x x 2 5 1 3 ⋅...

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1 Homework #1 IOE 316 - Introduction to Markov Processes - Winter 2010 Homework #1 (2 pages) Answers are due before start of class on Tuesday, March 16, 2010 1. A robot at a manufacturing plant occasionally fails. Each day, the robot is either up (operating state) or down (failed state). Transitions between states occur according to a stationary discrete-time Markov chain. The transition probability matrix for the robot between the up and down states, from one day to the next, is shown below. Up Down 4 . 0 6 . 0 1 . 0 9 . 0 Down Up (a) What is the transition probability matrix from Monday to Wednesday? (b) The probability that the robot is up on Wednesday is 85.2%. What was the probability that it was up on Monday? 2. Multiply the following matrices:

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Unformatted text preview: (a) ( ) ⋅ 1 3 2 5 x x = ? (b) ( ) x x 2 5 1 3 ⋅ = ? (c) ? 5 3 4 7 2 1 8 3 2 = ⋅ x 2 3. A stationary discrete-time Markov chain has 3 states, and the following transition probability matrix P from one step in time to the next (i.e, from time 0 to time 1) . = 4 . 6 . 9 . 1 . 5 . 3 . 2 . P (a) Sketch the state transition diagram for the Markov chain. (b) What is the transition probability matrix from time 0 to time 2 ? (c) What is the transition probability matrix from time 0 to time 4 ?...
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## This note was uploaded on 03/17/2010 for the course IOE 316 taught by Professor Dolinskaya during the Winter '08 term at University of Michigan.

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IOE+316+Homework+1 - (a ⋅ 1 3 2 5 x x =(b x x 2 5 1 3 ⋅...

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