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Is there literally any [ preferably free ] Computer Algebra System that would handle probability theory directly? As for now I am mainly interested in calculating marginal densities out of user-defined joint densities on diverse domains, but a complete system would be even better. And by any system I mean also that operating system is not an issue as long it works on one of the big three (Linux, Windows, Mac OS X).

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    Recommend you have a look at: http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems (it looks liker there are three choices and two of them are commercial, but any of the free ones can do these things - just not canned in the program, you have to do work and programming in that environment). HTH2012-09-19
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    @Amzoti If by doing work you mean to present an appropriate integral, then I can already do it in the CAS I currently use - namely wxMaxima. But the problem is that as for now I tend to make errors precisely in this step ( being still a student ) and among other things it is the very skill I want to practice2012-09-19
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    Well, what you ask about is just doing some integrals, and you do not need ny particular "probability functionality" to do that ...2012-09-19
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    Have you tried [R](http://www.r-project.org/)?2013-07-28

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