We give examples of piecewise linear random interval maps satisfying arcsine and Darling–Kac laws, which are analogous to Thaler’s arcsine and Aaronson’s Darling–Kac laws for the Boole transformation. They are constructed by random switch of two piecewise linear maps with attracting or repelling fixed points, which behave as if they were indifferent fixed points of a deterministic map.

We give an example of a piecewise linear random interval map satisfying arcsine and Darling-Kac laws, which are analogous to Thaler's arcsine and Aaronson's Darling-Kac laws for the Boole transform. It is constructed by random switch of two piecewise linear maps with attracting fixed points, which behave as if they were indifferent fixed points of a deterministic map.