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Assumptions is an option to Integrate. The message is telling you to add the assumption that x is real (by default, variables are usually treated as complex). f[x_] := Piecewise[{{1, -1/2 <= x <= 1/2}}, 0]; ProbabilityDistribution[ Integrate[f[a], {a, x - 1/2, x + 1/2}, Assumptions -> x ∈ Reals], {x, -2, 2}] For this simple example one ...



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