Apply the sum-product algorithm to a Bayesian network for the lung cancer problem described in Figure 2. The lung cancer dataset is available for download on the course homepage^{2}. See lungcancer.txt for a description of the data set. You are required to use MATLAB for this assignment.

- a)
- Write down the joint distribution over the five random variables and defined by the Bayesian network.
- b)
- All random variables in the graph are binary (or Boolean) variables
. The conditional distributions determined in a) can therefore be written in the form of the Bernoulli distribution
- c)
- Construct a factor graph from the Bayesian network.
- d)
- Apply the sum-product algorithm to the factor graph obtained in c) to calculate the joined distributions of the query variables (black circles) given the indicated evidence (gray circles) for each of the four problem settings shown in Figure 2. Assume that the observed random variables always have the value 1 (or true in case of Boolean variables).