Hw5_ORIE361_2008

# Hw5_ORIE361_2008 - ORIE 361/523 Homework 5 Instructor Mark...

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ORIE 361/523 – Homework 5 Instructor: Mark E. Lewis due February 27, 2008 (drop box) 1. One light bulb at the Rhodes student lounge has a maximum life of m days. In each day, the bulb will go crashed with probability p , in which case a new bulb must be installed to replace the broken one. Also a bulb that has survived for m days must be replaced according to the rule of maintenance. In the long run, what is the fraction of time that a student will ﬁnd a newly-installed fresh light bulb in the lounge? 2. Three cards a , b , c are placed in a row in one of six possible orders, and their order is changed successively as follows: A random choice of either the left-hand card or the right-hand card is made, the left-hand card being chosen with probability p = 1 2 , the right-hand card being chosen with probability q = 1 - p = 1 2 . The chosen card is then placed between the other two. For example, if the initial card order is bac , and the right-hand card is chosen, then after this choice, the card order becomes

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Hw5_ORIE361_2008 - ORIE 361/523 Homework 5 Instructor Mark...

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