This exercise is concerned with the variable elimination algorithm in Figure.

a. Section 14.4 applies variable elimination t the query P (Burglary?JohnCalls = true, Mary Calls = true). Perform the calculations indicated and check the answer is correct.

b. Count the number of arithmetic operations performed, and compares it with the number performed by the enumeration algorithm.

c. Suppose a network has the form of a chain: a sequence of Boolean variables X1... Xn where Parents (Xi) = {X i_1} for i = 2... n. What is the complexity of computing P (X1?Xn = true) using enumeration? Using variable elimination?

d. Prove that the complexity of running variable elimination on a poly-tree network is linear in the size of the tree for any variable ordering consistent with the network structure.

function ELIMINATION-ASK(X, e, bn) returns a distribution over X inputs: X, the query variable e, evidence specified as an event bn, a Bayesian network specifying joint distribution P(X1,..., X,) factors -[; vars - REVERSE(VARS[bn]) for each var in vars do factors [MAKE-FACTOR(var.e)lfactors] if var is a hidden variable then factors - SUM-OUT(var, factors) return NORMALIZE(POINTWISE-PRODUCT(factors))