#zero-probability

Question 1: Single choice

A model $Q$ assigns probability exactly $0$ to an outcome $x$ that has $p(x) > 0$ under the true distribution $P$ . What is $D_{\mathrm{KL}}(P \| Q)$ ?

Infinite, because the term for $x$ contains $\log \frac{p(x)}{0}$ 1
Unaffected, because the sum only runs over outcomes with $q(x) > 0$ 2
Zero for that term, because an impossible outcome carries no information3
Finite, and at most the logarithm of the number of outcomes4

Timed test