Question: Let Y1, . . . , Yn be iid Uniform(0, 1) random variables. Let Y(i) be the ith order statistic. (a) Derive the probability density

Let Y1, . . . , Yn be iid Uniform(0, 1) random variables. Let Y(i) be the ith order statistic.

  1. (a) Derive the probability density function of Y(i).
  2. (b) For 1 i < j n, derive the joint density of (Y(i), Y(j)).
  3. p
  4. (c) Show Y(n) 1 in probability.
  5. (d) Show that n(1Y(n)) converge in distribution to a limit. Identify the limiting distribution.

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