Artificial Intelligence Problem Description

The following Bayesian Network represents two causes and two effects related to Lung Cancer. Each variable takes the value true (t) or false (f). We will abbreviate the five variable names using their leading letters: P, S, C, X, and D. The probabilities shown are all for the is true outcome, e.g. read P(P=t) =0.90 as the probability that the variable Pollution takes the value true is 0.90. The probability that it is false is not shown, but is easily derived. 3 Requirements Note regarding the calculation, you should show your working process of the calculation to demonstrate that you know how to calculate them.

1. Using inference by enumeration to calculate the probability P(P = t|X = t) (i) describe what are the evidence, hidden and query variables in this inference, (ii) describe how would you use variable elimination in this inference, i.e. to perform the join operation and the elimination operation on which variables and in what order, and (iii) report the probability,

2. Given the Bayesian Network , find the variables that are independent to each other or conditionally independent given another variable. Find at least three pairs or groups of such variables.

3. If given the variable order as , draw a new Bayesian Network structure (nodes and connections only) to describe the same problem/domain as shown in the above given Bayesian Network. [hint: considering the above (conditionally) independent variables, the network should keep the original dependence between variables, which are that (conditionally) independent variables should remain being independent to each other, and dependent variables remain being dependent]. For each connection, explain why it is needed. 2 Relevant Data Files and Program Files