Calculations with random variables

I often need to do calculations such as the following:

• A, B, C, D are independent random variables distributed uniformly in [0,1].
• X := A+B and Y:=B+C+D.
• What is the probability that X < Y?
• What is the expected value of Y, given that Y < 2?
• etc...

I thought that it might be possible with Python scipy, since it has a random-variable class. But, I did not find e.g. how to create a random-variable that is the sum of two given random-variables, or the conditional distribution of another variable.

Is there another library tool that can do such calculations easily?

_{Note: I asked a similar question in math.SE, with no replies so far.}