Non-Gaussian noise often causes in significant performance abatement for systems which are designed using Gaussian assumption. This report challenges the question of General Linear Model with White Gaussian Noise assumption in order to define the sensitivity of the performance of an optimal estimator. Gaussian noise models provide an important role in many signal processing applications. The Laplacian and Uniform signal are two worthy examples of noise that can be compared to the White Gaussian Noise, though the sensitivity which can be compared with any non-Gaussian. White Gaussian Noise has been considered for General Linear Models and deviation from whiteness would affect on our estimates under different circumstances. Moreover, new assumptions have been considered to generate different type of signals in order to evaluate the sensitivity of the General Linear Model.