When faced with an f(x), F(x), or S(x) that looks difficult to integrate, what is a recommended approach?

• A. Check the exhibit for a generic distribution formula and identify where x appears
• B. Ignore and proceed with a random guess
• C. Immediately perform numeric integration
• D. Approximate using a normal distribution only

Answer: (A)

When you see an integral involving a density f(x), a distribution function F(x), or a survival function S(x), the fastest and most reliable move is to check the exhibit for a generic distribution formula and identify where x appears. Exhibits often compile standard results for common distributions—showing how integrals map to probabilities, CDFs, or moments like E[X]—so you can substitute the relevant formula directly instead of grinding through the integration. This approach uses the distribution’s built-in relationships, giving you the exact result tied to the model at hand. It’s better than guessing, and it’s more precise than jumping to numeric integration or defaulting to a normal approximation unless the problem specifically justifies it.