Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 223 / 1 / a / Solution

Let $m=F^{-1}(1/2)$ be the unique median. The influence function of the sample median isaway from $m$. Its second moment, equivalently the asymptotic distribution of a sample median, givesNo symmetry assumption is used: the density is evaluated at the actual median of $F$.