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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2016 • Question 2

Question

Math 6010 • Linear Models Spring 2016 • Question 2

Let \(X_1,\ldots ,X_n\) be iid exponential(1) random variables. Find the joint pdf of the pair \((X_{(1)},X_{(3)})\), where \(X_{(i)}\) denotes the \(i\)th order statistic, i.e. \[ X_{(1)}\leq X_{(2)}\leq \cdots \leq X_{(n)}. \]

Raw LaTeX

Let \(X_1,\ldots,X_n\) be iid exponential(1) random variables. Find
the joint pdf of the pair \((X_{(1)},X_{(3)})\), where \(X_{(i)}\) denotes the
\(i\)th order statistic, i.e.
\[
  X_{(1)}\leq X_{(2)}\leq \cdots\leq X_{(n)}.
\]

Topic Tags

Estimator Distributions Exponential Martingales Measure-Theoretic Probability Uniform Integrability and Truncation Methods