  We present a maximum entropy framework to separate intrinsic and extrinsic
contributions to noisy gene expression solely from the profile of expression.
We express the experimentally accessible probability distribution of the copy
number of the gene product (mRNA or protein) by accounting for possible
variations in extrinsic factors. The distribution of extrinsic factors is
estimated using the maximum entropy principle. Our results show that extrinsic
factors qualitatively and quantitatively affect the probability distribution of
the gene product. We work out, in detail, the transcription of mRNA from a
constitutively expressed promoter in {\it E. coli}. We suggest that the
variation in extrinsic factors may account for the observed {\it wider than
Poisson} distribution of mRNA copy numbers. We successfully test our framework
on a numerical simulation of a simple gene expression scheme that accounts for
the variation in extrinsic factors. We also make falsifiable predictions, some
of which are tested on previous experiments in {\it E. coli} while others need
verification. Application of the current framework to more complex situations
is also discussed.
