Let S be a set of n points distributed uniformly and independently in the unit square. Then the expected number of empty four-gons with vertices from S is T(n^2 log¿ n). A four-gon is empty if it contains no points of S in its interior.
Fabila-Monroy, R.; Huemer, C.; Mitsche, D. The number of empty four-gons in random point sets. "Electronic notes in discrete mathematics", 2014, vol. 46, p. 161-168.