Compute a Complex Probability
Compute the probability of an event that is represented by a region in the complex plane.
prob = Probability[2 x < Abs[x ^ 2 + I y] < 5, {x, y}ProductDistribution[{UniformDistribution[{-3, 7}], 2}]];Labeled[RegionPlot[2 x < Abs[x ^ 2 + I y] < 5, {x, -2.5, 2.5}, {y, -5, 5}, Mesh -> 10, PlotStyle -> Hue[.6, .3, .9], ImageSize -> 350], Style[Row[{TraditionalForm[Pr[2 x < Abs[x ^ 2 + I y] < 5]], TraditionalForm[prob]}, "="], FontFamily -> "Verdana"]]