  We explore the link between combinatorics and probability generated by the
question "What does a random parking function look like?" This gives rise to
novel probabilistic interpretations of some elegant, known generating
functions. It leads to new combinatorics: how many parking functions begin with
$i$? We classify features (e.g., the full descent pattern) of parking functions
that have exactly the same distribution among parking functions as among all
functions. Finally, we develop the link between parking functions and Brownian
excursion theory to give examples where the two ensembles differ.
