Question: Let \({{X}_{1}},{{X}_{2}},...,{{X}_{n}}\) be n independent RV with the same distribution function \(F\)

(a) Prove that for any numbers \({{x}_{1}},...,{{x}_{n}}\)

\[\min \left\{ {{x}_{1}},...,{{x}_{n}} \right\}=-\max \left\{ -{{x}_{1}},...,-{{x}_{n}} \right\}\]

(b) Let \(Z=\max \left\{ {{X}_{1}},...,{{X}_{n}} \right\}\) and \(V=\min \left\{ {{X}_{1}},..,{{X}_{n}} \right\}\)