Q3)

Consider four binary variables A, B, C, D. The Directed Acyclic Graph (DAG) shown below describes the relationship between these variables along with their conditional probability tables (CPT). 

3.1) In the above network, state why A is independent of B with reasons, i.e., A⊥B.

3.2) Hence, obtain an expression (in a simplified form) for P(D=1|A=1, B=1) in terms of  beta only.

3.3) The table shown below provides 20 simulated data obtained for the above Bayesian network. Use this data to find the maximum likelihood estimates of a,b, y and theta.

3.4) Find the value of P(D=1|A=1, B=1) using the values obtained for b from the above question Q3.3.