Statistics Solutions

(See Solution) Let X_1,X_2,...,X_n be n independent RV with the same distribution function F Prove that for any numbers x_1,...,x_n min x_1,...,x_n =-max

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

  1. Prove that for any numbers \({{x}_{1}},...,{{x}_{n}}\)
    \[\min \left\{ {{x}_{1}},...,{{x}_{n}} \right\}=-\max \left\{ -{{x}_{1}},...,-{{x}_{n}} \right\}\]
  2. Let \(Z=\max \left\{ {{X}_{1}},...,{{X}_{n}} \right\}\) and \(V=\min \left\{ {{X}_{1}},..,{{X}_{n}} \right\}\)

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