A stick of length 1 is randomly broken, which means that the remaining piece is U(0, 1)-distributed. The remaining piece is broken similarly, and so on.
(a) Let Xn be the length of the piece that remains after the stick has been broken n times. Describe Xn as a product.
(b) Prove that
and determine the limit.
(c) Find the distribution of the length of the first piece that was thrown away - don't compute, think! Then compute.