Q1:

Again consider the Bayesian network structure in Figure 1 and the associated conditional probability tables

(CPTS) below. Assume all variables are binary.

a) Write down the expression for the probability P(A-1 | B-1,C= 0) in terms of the parameters

shown in the above CPTs.

b) Suppose you are given the training data in Table 2. What is the log-likelihood function of above

Bayesian network given this data? Note: it should be a function of the parameters shown in the above

CPTS.

c) Optimize the log-likelihood function from part (b) to obtain the maximum-likelihood parameters

for this Bayesian network. Please show your work.

d) Consider an alternative Bayesian network structure shown in Figure 2. Would the likelihood

achieved by this BN be at least that of the BN from part (c), or would it be smaller? Justify your an-

swer.