Q$2$ If $n=2m-1$ is odd, and the observations $\{x_1,$dots,$x_n\}$ are distinct, then the sam$-$

ple median $x(m)$ is uniquely defined. Prove that a bootstrap resample $\{x_1^{**},$dots,$x_n^{**}\}$ has

median $x_m^{**}$ with distribution function

$G_n^{**}(x_{(k)})=Pr(x_{(m)}^{**}{x}_{(k)})={\displaystyle \underset{j=m}{\overset{n}{}}}([n],[j])\frac{k^j(n-k{)}^{(n-j)}}{n^n}$