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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2015 • Question 2

Question

Math 6010 • Linear Models Spring 2015 • Question 2

Let \(X\geq 0\) and \(\mathbb {E}|X|^p<\infty \) with some \(p>0\). Show that \[ \lim _{t\to \infty } t^p\mathbb {P}\{X>t\}=0. \]

Raw LaTeX

Let \(X\geq0\) and \(\E|X|^p<\infty\) with some \(p>0\). Show that
\[
  \lim_{t\to\infty} t^p\Prob\{X>t\}=0.
\]

Topic Tags

Uniform Integrability and Truncation Methods