For the Lego discrepancy with M bins, which is equivalent with a
chi^2-statistic with M bins, we present a procedure to calculate the moment
generating function of the probability distribution perturbatively if M and N,
the number of uniformly and randomly distributed data points, become large.
Furthermore, we present a phase diagram for various limits of the probability
distribution in terms of the standardized variable if M and N become infinite.Comment: 16 page