Exercise 6.5 In this question, you will build a belief network representation of the Deep Space 1 (DS1) spacecraft considered in Exercise 5.10 (page 212). Figure 5.14 (page 213) depicts a part of the actual DS1 engine design.

Suppose the following scenario:
• Valves can be open or closed.
• A value can be ok, in which case the gas will flow if the valve is open and not if it is closed; broken, in which case gas never flows; stuck, in which case gas flows independently of whether the valve is open or closed; or leaking, in which case gas flowing into the valve leaks out instead of flowing through.
• There are three gas sensors that can detect gas leaking (but not which gas);
the first gas sensor detects gas from the rightmost valves (v1 . . . v4), the second gas sensor detects gas from the center valves (v5 . . . v12), and the third gas sensor detects gas from the leftmost valves (v13 . . . v16).

(a) Build a belief-network representation of the domain. You only must consider the topmost valves (those that feed into engine e1). Make sure there are appropriate probabilities.

(b) Test your model on some non-trivial examples.