Estimate, by standard procedures, means, variances and covariances.

To fit a Multivariate Gaussian Distribution you can compute the mean and variance with MLE to get the mean vector and covariance matrix. But the fact that three random variables have a normal distribution does not imply that the three variables has a joint normal distribution.

Thank you very much for your replies Vladimir and Antonio.

First, I must apologize for my lack of knowledge on perhaps the most basic fundamentals of statistical analysis if the questions I am going to ask seem trivial.

When you said MLE, did you mean Maximum Likelihood Estimation? 

I referred to the book “Methods of Multivariate Analysis" 2nd Edition by Alvin Rencher. In page 90, there is a section titled "estimation in the multivariate normal" which I have uploaded to this thread. From what I understood, a multivariate normal distribution can be estimated if I have n observation vectors of D dimensions. In my case, since I have three different 1D distributions, the number of samples of each distribution may be different in which case I won't be able to make observation vectors of 3D to carry out the estimation. What approach should I adopt?

Perhaps, I am going in a totally wrong direction.

I would be very grateful if you could provide me with a reference of the method you have mentioned. (If possible, a book with some working examples will be perfect.)

Thanking you in advance.

As I understand you have three normally distributed random variables and you are interested in constructing a multivariate distribution of then. In Kenney, J. F. and Keeping, E. S, Mathematics of Statistics, Princenton (1951), you have the mathematical fundamentals for two variables, but it's very simple to extend to n variables. 

If you use the Wolfram's sofware "Mathematica" in this page you can see an introduction to the process with references to the commands that you might use in that software ( http://mathworld.wolfram.com/BivariateNormalDistribution.html).

http://mathworld.wolfram.com/BivariateNormalDistribution.html

Thank you very much for your detailed answer. It is very helpful.