What are the limitations of the full joint distribution for uncertain reasoning?

Question
II. Reasoning under uncertainty

1. What are the limitations of the full joint distribution for uncertain reasoning?

2. Show that

3. Show that the statement P(A,B|C)=P(A|C)P(B|C)is equivalent to either of the statements: P(A|B,C)=P(A|C) and P(B|A,C)=P(B|C)

4. Consider the following cell phone domain. Having a charged battery (CB) enables a cell phone to be operational (PO). Having an operational cell phone, being in the coverage area (CA), and knowing the number to call (KN) enables the placing of a call (PC). Assume there are no other dependencies. All random variables are Boolean.

a.Draw the Bayesian Network for this domain, including nodes, arcs and the form of each conditional probability table (CPT) at each node.

b. Compare the number of independent specifiable probabilities in the full joint probability distribution table entries and the numbers required by the BN.

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