# From built-in symbols to algebraic representation

If I have an expression with Mathematica's built-in functions like

Probability[x > 0, x \[Distributed] UniformDistribution[{-1, 1}]]


its algebraic representation would be something like

Integrate[PDF[UniformDistribution[{-1, 1}], x], {x, 0, \[Infinity]}]


If I understand correctly, Mathematica's engine does the transformation from first to second representation and then evaluates it.

Is there a function that will take as input first expression and give me the second?

• It does not appear that Mathematica takes the straightforward path. Evaluate Probability[x > 0, x \[Distributed] UniformDistribution[{-1, 1}]] // Trace – Bob Hanlon Jan 15 '16 at 14:04
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• @BobHanlon Ok thanks so it's much more complex than I imagined. Maybe what I'm asking is not possible, or just in some very simple cases. – Gleb Jan 15 '16 at 14:12
• Sometimes these things are done by table lookup. That seems likely with common, simple distributions like UniformDistribution. – Michael E2 Jan 15 '16 at 14:18

{pred, var, dist} = {x>0, x, UniformDistribution[{-1, 1}]}

Probability[pred, Distributed[var, dist] ==