On the Gaussian assumption

This had been pending for over an year now.

Issue:
In many cases for a random variable, given the knowledge of the first two moments (i.e. mean and variance) and faced with the need of assuming a probability density function (pdf), it is common to taken it to be Gaussian.

What I knew:
The assumption of Gaussian distribution in many cases can be justified on the basis of the central limit theorem. Also, the Gaussian pdf is completely characterized using the first two moments i.e. the mean and variance.

Another reason which I came to know while reading about estimation and filtering:
Given the mean and variance the Gaussian distribution has the maximum entropy.

Ref:
Catlin, D. E. (1988) "Estimation control and the discrete Kalman filter", Springer.
Shannon, C. E. (1948) "A mathematical theory of communication" (As available in the pdf format from: http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html).