AA228/CS238: Decision Making under Uncertainty
Autumn 2017
Prof. Mykel J. Kochenderfer • Durand 255 • email:
MIDTERM 1 Due date: October 11
You have 60 minutes to complete this exam. You may use one page of notes (front and back) but no
other resources. All questions are weighted equally.
Question 1. Suppose we have a Bayesian network A → B → C ← D ← E. Each variable takes on one of
three possible values. Add one or more directed edges so that the resulting Bayesian network has exactly 38
independent parameters defining the joint distribution. Draw the resulting Bayesian network.
Question 2. Suppose we have a Bayesian network with edges A → B ← C → D and B → E → F . All
variables are binary and we know P (a0) = 0.5 and P (d0 | a0) = 0.3. What is P (d1 | a1)? Why?
Question 3. Suppose we want to infer whether the baby is hungry (H) based on whether we recently fed
the baby (F ) and whether the baby is crying (C). We will represent the joint distribution P (H,F,C) by a
Bayesian network F → H → C. We assume P (h1 | f1) = 0.3, P (c1 | h1) = 0.4, and P (c1 | h0) = 0.2. What
is the probability that the baby is hungry given that we recently fed the baby and the baby is crying?
Question 4. Suppose we use likelihood weighted sampling to answer the previous question. Produce one
possible sample, specifying the assignment of variables to values, and calculate its associated weight.
Question 5. Suppose we have six data points corresponding to observations of whether I sing (S) and
whether my baby cries (C). Write down a plausible set of data points in a table such that half the nights I
sing, half the nights the baby cries, and the maximum likelihood estimate of P (s1, c1) from our data is 1/3.
Question 6. Your professor wears a single shirt per lecture. The color of the shirt is represented by a
random variable C, which may take on values white, blue, and other. The probability of each outcome is
denoted θwhite, θblue, and θother. Suppose we use a Dirichlet distribution to model the joint distribution
P (θwhite, θblue, θother). What might be a sensible set of parameters to use for the Dirichlet distribution if we
want to capture strong confidence that he wears white and blue shirts equally often and very seldom wears
shirts of other colors?
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