The question provides two functions $A(n)$ and $W(n)$, representing the worst-case and average-case running times of an algorithm. It asks which asymptotic relation among Big O, Theta (Θ), Omega (Ω), and Little o would be correct regarding these two functions.

Let's analyze the options:

1. $A(n) = O(W(n))$: This notation implies that the average-case running time $A(n)$ grows asymptotically no faster than $W(n)$. However, typically, we expect the worst-case time $W(n)$ to be equal to or larger than the average-case time $A(n)$, so this statement may not hold unless $A(n)$ is indeed bounded by $W(n)$.

2. $A(n) = \Omega(W(n))$: This notation implies that the average-case running time $A(n)$ grows at least as fast as $W(n)$. This would imply that the average-case performance is at least as bad as the worst case, which is generally unusual.

3. $A(n) = \Theta(W(n))$: This notation implies that the average-case running time $A(n)$ and the worst-case running time $W(n)$ grow at the same rate. This could be true if the algorithm’s performance in both cases is relatively close or similar.

4. $A(n) = o(W(n))$: This notation implies that $A(n)$ grows strictly slower than $W(n)$, meaning that the average case is always better than the worst case asymptotically. This is generally the most common scenario, as the worst case is expected to be greater than the average case.

Based on standard algorithm analysis, option 4 ($A(n) = o(W(n))$) is usually correct because, in most scenarios, the average case is asymptotically smaller than the worst case.

Answer: Option 4 - $A(n) = o(W(n))$