  We study the counting statistics of charge transport in the Anderson impurity
model (AIM) employing both Keldysh perturbation theory in a Fermi liquid
picture and the Bethe ansatz. In the Fermi liquid approach, the object of our
principal interest is the generating function for the cumulants of the charge
current distribution. We derive an exact analytic formula relating the full
counting statistic (FCS) generating function to the self-energy of the system
in the presence of a measuring field. We first check that our approach
reproduces correctly known results in simple limits, like the FCS of the
resonant level system (AIM without Coulomb interaction). We then proceed to
study the FCS for the AIM perturbatively in the Coulomb interaction. By
comparing this perturbative analysis with a strong coupling expansion, we
arrive at a conjecture for an expression for the FCS generating function at
O(V^3) (V is the voltage across the impurity) valid at all orders in the
interaction.
  In the second part of the article, we examine a Bethe ansatz analysis of the
current noise for the AIM. Unlike the Fermi liquid approach, here the goal is
to obtain qualitative, not quantitative, results for a wider range of voltages
both in and out of a magnetic field. Particularly notable are finite field
results showing a double peaked structure in the current noise for voltages
satisfying eV ~ mu H$. This double peaked structure is the ``smoking gun'' of
Kondo physics in the current noise and is directly analogous to the single peak
structure predicted for the differential conductance of the AIM.
