We break a unit length rod into two pieces at a uniformly chosen point. Find the expected length of the smaller piece We break a unit length rod into two pieces at a uniformly chosen point. Find the
expected length of the smaller piece

With probability ${1\over2}$ each the break takes place in the left half, resp. in the right half of the rod. In both cases the average length of the smaller piece is ${1\over4}$. Therefore the overall expected length of the smaller piece is ${1\over4}$.
