  We analyse the noise of the edge current of a generic fractional quantum Hall
state in a tunnelling point contact system. We show that the non-symmetrized
noise in the edge current for the system out-of-equilibrium is completely
determined by the noise in the tunnelling current and the Nyquist-Johnson
(equilibrium) noise of the edge current. Simply put, the noise in the
tunnelling current does not simply add up the equilibrium noise of the edge
current. A correction term arises associated with the correlation between the
tunnelling current and the edge current. We show, using a non-equilibrium Ward
identity, that this correction term is determined by the anti-symmetric part of
the noise in the tunnelling current. This leads to a non-equilibrium
fluctuation-dissipation theorem and related expressions for the excess and shot
noise of the noise in the edge current. Our approach makes use of simple
properties of the edge, such as charge conservation and chirality, and applies
to generic constructions of the edge theory which includes edges of non-Abelian
states and edges with multiple charged channels. Two important tools we make
use of are the non-equilibrium Kubo formula and the non-equilibrium Ward
identity. We discuss these identities in the appendix.
