  A general fundamental relation connecting the correlation of Stokes and
anti-Stokes modes to the quantum statistical behavior of vibration and pump
modes in Raman-active materials is derived. We show that under certain
conditions this relation can be used to determine the equilibrium number
variance of phonons.Time and temperature ranges for which such conditions can
be satisfied are studied and found to be available in todays' experimental
standards. Furthermore, we examine the results in the presence of multi-mode
pump as well as for the coupling of pump to the many vibration modes and
discuss their validity in these cases.
