Correlation analysis of gamma-ray data with varying sensitivities

A gamma-ray source is defined as a significant excess of the correlated count or the correlated flux over the underlying background. Therefore, the most important information from cross-correlating the raw data for accepting or rejecting a point source as a gamma-ray source is the correlated strength of the source expressed in the correlated counts or the correlated flux and the parent standard deviation of the underlying background. Exact expressions are derived here for the standard deviation of the correlated flux and the parent standard deviation of the underlying background of a gamma-ray excess in a correlation analysis. The advantage of these expressions over the ones previously used is that they are exact and that their derivations do not need the assumption that the sensitivity values for all the sky bins in the matrix over which cross-correlation is done are the same