  The Full Counting Statistics (FCS) is studied for a one-dimensional system of
non-interacting fermions with and without disorder. For two unbiased $L$ site
lattices connected at time $t=0$, the charge variance increases as the natural
logarithm of $t$, following the universal expression $<\delta N^2> \approx
\frac{1}{\pi^2}\log{t}$. Since the static charge variance for a length $l$
region is given by $<\delta N^2> \approx \frac{1}{\pi^2}\log{l}$, this result
reflects the underlying relativistic or conformal invariance and dynamical
exponent $z=1$ of the disorder-free lattice. With disorder and strongly
localized fermions, we have compared our results to a model with a dynamical
exponent $z \ne 1$, and also a model for entanglement entropy based upon
dynamical scaling at the Infinite Disorder Fixed Point (IDFP). The latter
scaling, which predicts $<\delta N^2> \propto \log\log{t}$, appears to better
describe the charge variance of disordered 1-d fermions. When a bias voltage is
introduced, the behavior changes dramatically and the charge and variance
become proportional to $(\log{t})^{1/\psi}$ and $\log{t}$, respectively. The
exponent $\psi$ may be related to the critical exponent characterizing
spatial/energy fluctuations at the IDFP.
