  We present a theory for the number fluctuations of a quasi-two-dimensional
(quasi-2D) dipolar Bose-Einstein condensate measured with finite resolution
cells. We show that when the dipoles are tilted to have a component parallel to
the plane of the trap, the number fluctuations become anisotropic, i.e. depend
on the in-plane orientation of the measurement cell. We develop analytic
results for the quantum and thermal fluctuations applicable to the cell sizes
accessible in experiments. We show that as cell size is increased the
thermodynamic fluctuation result is approached much more slowly than in
condensates with short range interactions, so experiments would not require
high numerical aperture imaging to observe the predicted effect.
