1. Section exact-inference-section applies variable elimination to the query $${\textbf{P}}({Burglary}{JohnCalls}{true},{MaryCalls}{true})\ .$$ Perform the calculations indicated and check that the answer is correct.

2. Count the number of arithmetic operations performed, and compare it with the number performed by the enumeration algorithm.

3. Suppose a network has the form of a

*chain*: a sequence of Boolean variables $X_1,\ldots, X_n$ where ${Parents}(X_i)\{X_{i-1}\}$ for $i2,\ldots,n$. What is the complexity of computing ${\textbf{P}}(X_1X_n{true})$ using enumeration? Using variable elimination?

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

Consider the variable elimination algorithm in
Figure elimination-ask-algorithm (page elimination-ask-algorithm).

1. Section exact-inference-section applies variable
elimination to the query
$${\textbf{P}}({Burglary}{JohnCalls}{true},{MaryCalls}{true})\ .$$
Perform the calculations indicated and check that the answer
is correct.

2. Count the number of arithmetic operations performed, and compare it
with the number performed by the enumeration algorithm.

3. Suppose a network has the form of a *chain*: a sequence
of Boolean variables $X_1,\ldots, X_n$ where
${Parents}(X_i)\{X_{i-1}\}$ for $i2,\ldots,n$.
What is the complexity of computing
${\textbf{P}}(X_1X_n{true})$ using
enumeration? Using variable elimination?

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