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Random Variable Calculus Using Computer Algebra

Does anyone know of a good way to compute variances (or higher moments) of
functions of random variables in Mathematica.

For example:   Var[ X + Y] = Var[X] + Var[Y] + 2 * Corr_xy * Sqrt(Var[X] *

is easy enough to do by hand.  But what about an expression like Var[ X * Y
+ Y * Z + X * Z] ?? I have a strong interest in learning how to do this in
Mathematica (or another computer algebra program).  If anyone know how, feel
free to email me directly at:  johnevans at

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