#### 0rthodontist

Science Advisor

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Code:

```
function Enumeration-Ask(X, e, bn) returns a distribution over X
inputs: X, the query variable
e, observed values for variables E
bn, a Bayes net with variables {X} u E u Y /* Y = hidden variables */
Q(X) <- a distribution over X, initially empty
for each value xi of X do
extend e with value xi for X
Q(xi) <- Enumerate-All(Vars[bn], e)
return Normalize(Q(X))
function Enumerate-All(vars, e) returns a real number
if Empty?(vars) then return 1.0
Y <- First(vars)
if Y has value y in e
then return P(y | parents(Y)) * Enumerate-All(Rest(vars), e)
else return the sum over y of P(y | parents(Y)) * Enumerate-All(Rest(vars), ey)
where ey is e extended with Y = y
```