CS2710 / ISSP 2160: Homework 6
Uncertainty and Probabilistic Reasoning
(Chapters 13-14)
Assigned: November 17, 2009
Due: December 8, 2009
1. Probability (15 pts)
13.6 (Russell and Norvig, p. 489)
2. Probability (15 pts)
Of the entire population, 2% has a certain disease X. A test Y, which
indicates whether or not a person has the disease, is not 100%
accurate. If a person has the disease, there is a 6% chance that it
will go undetected by the test. However, there is also a 9% chance of
"false alarm" (meaning that the person does not have the disease but
the test indicates otherwise). A person Z takes a test which later
comes out positive (meaning that the test says he has the
disease). What is the probability of this person having the disease in
reality?
3. Probability (15 pts)
Random variables A,B are conditionally independent given C when
P(A,B|C) = P(A|C)P(B|C). Prove that this implies
P(A|B, C) = P(A|C).
4. Bayesian Networks (20 pts)
14.1 a,c,d (Russell and Norvig, p. 533). Here is some relevant car
knowledge: Icy weather is not caused by any car-related variables,
but it directly affects the battery and the starter motor. The starter
motor in turn directly impacts whether the car starts.
In addition, answer the following question using the original
network topology (that is in Figure 14.18) rather than the extension
used above.
Give the expression for the full joint probability
for: Battery=T, Radio=T, Ignition=T, Gas=F, Starts=T, Moves=F.
5. More Bayesian Networks (15 pts)
Again consider the Bayesian network in Figure 14.18.
(a) Assume we want to compute the probability of the car not moving, that
is P(Moves = False). Write down the expression for computing the
probability from conditionals via the blind approach.
(b) Write down a more efficient expression for computing P(Moves =
False) that interleaves sums and products.
(c) Can we further speed up this computation by eliminating irrelevant
variables (because the summations equal 1 by definition)? Explain.