Abstract: Dirac ensembles lie at the intersection of random matrix theory and noncommutative geometry. In particular, we look at the (0,1) fuzzy Dirac ensemble with fermion in the case where the fermion mass is positive. We give an introduction to random matrix models, both analytic and formal, including the relationship between matrix integrals and generating functions of maps in the formal case. We also motivate and introduce the concept of a spectral triple from noncommutative geometry. One application of spectral triples is Dirac ensembles, consisting of a certain finite spectral triple with a probability distribution on the space of Dirac operators. Dirac ensembles describe a toy model of quantum gravity. We describe Dirac ensembles and their underlying hermitian matrix models, giving special attention to the (0,1) fuzzy Dirac ensemble with a fermion. The Schwinger-Dyson equations for this model can be found through complex analytic techniques, and allows for a perturbative solution of the moments. In the case where the potential is Gaussian, an exact solution for moments can be obtained using complex analytic techniques and elliptic integrals.