In smart grid paradigm, the consumer demands are random and time-dependent, owning towards stochastic probabilities. The stochastically varying consumer demands have put the policy makers and supplying agencies in a demanding position for optimal generation management. The utility revenue functions are highly dependent on the consumer deterministic stochastic demand models. The sudden drifts in weather parameters effects the living standards of the consumers that in turn influence the power demands. Considering above, we analyzed stochastically and statistically the effect of random consumer demands on the fixed and variable revenues of the electrical utilities. Our work presented the Multi-Variate Gaussian Distribution Function (MVGDF) probabilistic model of the utility revenues with time-dependent consumer random demands. Moreover, the Gaussian probabilities outcome of the utility revenues is based on the varying consumer n demands data-pattern. Furthermore, Standard Monte Carlo (SMC) simulations are performed that validated the factor of accuracy in the aforesaid probabilistic demand-revenue model. We critically analyzed the effect of weather data parameters on consumer demands using correlation and multi-linear regression schemes. The statistical analysis of consumer demands provided a relationship between dependent (demand) and independent variables (weather data) for utility load management, generation control, and network expansion.