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CS221 Exercise Set 7
1
CS 221, Autumn 2007
Exercise Set 7: Bayesian Networks
1.
Bayesian Networks and Chocolate
Suppose you’re watching chocolate being produced on a conveyor belt in a factory. There
are two levers controlling production, one that controls whether the chocolate is plain or
almond, and another that controls whether there is coconut or not. The levers stay in the
position they’re in with probability .7 and switch to the other setting .3, the two levers
operating independently. At the start of the day, the lever is in either setting with equal
probability.
From observing the conveyor belt, you can only tell what color the chocolate is, and have
the following table of probabilities for the color given what’s inside.
Inside
P(Color=Light

Inside)
P(Color=Dark

Inside)
Plain
0.1
0.9
Almond
0.3
0.7
Coconut
0.8
0.2
Almond + Coconut
0.9
0.1
Let
X
i
represent the state of the two levers at time step
i
, and let
Y
i
represent the ob
servation at time step
i
. So, the domain of
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This note was uploaded on 11/30/2009 for the course CS 221 taught by Professor Koller,ng during the Winter '09 term at Stanford.
 Winter '09
 KOLLER,NG
 Artificial Intelligence

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