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Hw2-ORIE3510_S12

# Hw2-ORIE3510_S12 - ORIE 3510 Homework 2 Instructor Mark E...

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ORIE 3510 – Homework 2 Instructor: Mark E. Lewis due 2PM, Wednesday February 8, 2012 (ORIE Hallway drop box) 1. Give the transition diagrams for the Markov chains with the given transition matrix: (a) P = ± 0 . 3 0 . 7 0 . 5 0 . 5 ² (b) P = 1 0 0 1 / 2 0 1 / 2 1 / 2 1 / 4 1 / 4 (c) P = 1 / 4 1 / 4 1 / 4 1 / 4 0 1 / 3 1 / 3 1 / 3 0 0 1 / 2 1 / 2 0 0 0 1 2. Consider an experiment in which 4 coins are tossed. Each of the coins has the probability of 0.4 of showing heads. In each step, n = 1 , 2 ,... , you toss the coins (among the 4 coins) that show up as tails in the previous step. If all the coins are heads in the previous step, then you toss all of the 4 coins. For example, if in step n , you see that two coins are heads and the other two are tails, then in step n +1, you will toss the two coins that just showed up as tails, leaving the head coins untouched. If, however, all the coins show up as heads in step n , you toss all the four coins in step n + 1. Let

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Hw2-ORIE3510_S12 - ORIE 3510 Homework 2 Instructor Mark E...

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