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
newlyinstalled 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 lefthand card or the righthand card
is made, the lefthand card being chosen with probability
p
=
1
2
, the righthand 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 righthand card is chosen, then after this
choice, the card order becomes
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 Spring '07
 LEWIS,M.
 yn, Markov chain, stationary distribution

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