In recent decades the Perron-Frobenius operator has proven to be a powerful tool in the studying of statistical properties of dynamical systems. By studying the operator's spectral properties one can make precise the analogy between chaotic systems and random processes. In particular, a framework centered about the operator has been developed for obtaining statistical laws for sufficiently chaotic systems e.g. a law of large numbers, central limit theorem, or large deviation principle; this is the so-called `functional analytic' approach. We will provide an accessible overview of this approach in the simple setting of piecewise expanding maps on the unit interval.