A scaled version of the curve is the probability density function of the Cauchy distribution. This is the probability distribution on the random variable formula_10 determined by the following random experiment: for a fixed point formula_11 above the formula_10-axis, choose uniformly at random a line through formula_11, and let formula_10 be the coordinate of the point where this random line crosses the axis. The Cauchy distribution has a peaked distribution visually resembling the normal distribution, but its heavy tails prevent it from having an expected value by the usual definitions, despite its symmetry. In terms of the witch itself, this means that the formula_10-coordinate of the centroid of the region between the curve and its asymptotic line is not well-defined, despite this region's symmetry and finite area.