Multivariate Random Variables

Here is the cdf, namely :

Here is , the covariance between and :

More generally, here is the variance-covariance matrix:

Here is the marginal pdf of :

Here is the conditional pdf of , given :

Here is the bivariate mgf :

Differentiating the mgf is one way to derive moments. Here is the product moment :

which we could otherwise have found directly with:

Multivariate transformations pose no problem to mathStatica either. For instance, let and denote transformations of and . Then our transformation equation is:

Using Transform, we can find the joint pdf of random variables and , denoted :

while the extremum of the domain of support of the new random variables are: