Let an individuals preferences be described by the RDEU criterion with (p) = 1(1 p) .

Let an individual’s preferences be described by the RDEU criterion with Ψ(p) = 1−(1− p)^β. In other words, Ψ(p) is close to a power function for p close to one, that is, for p’s corresponding to large values of r.v.’s. Let X be an exponential r.v. with a distribution F. Show that in this case, the transformation of F corresponds to dividing X by β.