Let [An,Bn] be random subintervals of [0,1] defined recursively as follows. Let A1=0, B1=1 and take Cn, Dn to be the minimum and maximum of k, i.i.d. random points uniformly distributed on [An,Bn]. Choose [AnÅ+1,BnÅ+1] to be [Cn,Bn] or [Cn,Dn] with probabilities p, q, r respectively, p+q+r=1. It is shown that the limiting distribution of [An,Bn] has the beta distribution on [0,1] with parameters k(p+r) and k(q+r). The result is used to consider a randomized version of Golden Section search.
