  We demonstrate that measurements of number fluctuations within finite cells
provide a direct means to study fluctuation scaling in a trapped two-component
condensate. This quantum system supports a second-order phase transition
between miscible (co-spatial) and immiscible (symmetry-broken) states that is
driven by a diverging susceptibility to magnetic fluctuations. As the
transition is approached from the miscible side the magnetic susceptibility is
found to depend strongly on the geometry and orientation of the observation
cell. However, a scaling exponent consistent with that for the homogenous gas
($\gamma = 1$) can be recovered, for all cells considered, as long as the fit
excludes the region in the immediate vicinity of the critical point. As the
transition is approached from the immiscible side, the magnetic fluctuations
exhibit a non-trivial scaling exponent $\gamma \simeq 1.30$. Experimentally,
the observation cells may be formed either by considering individual imaging
pixels or by combining pixels to form larger cells, and fluctuation statistics
can be obtained by repeated \emph{in situ} images. Interestingly, on both sides
of the transition, we find it best to extract the exponents using an
observation cell that covers half of the trapped system. This implies that
relatively low-resolution \emph{in situ} imaging will be adequate for the
investigation of these exponents. We also investigate the gap energy and find
exponents $\nu z$ = 0.505 on the miscible side and, unexpectedly, $\nu z$ =
0.60(3) for the immiscible phase.
