1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probability function question

  1. Sep 28, 2012 #1
    Hi guys, I have a question.

    E(|X|) < infinity iff E|X|I(|X| > n) -> 0 as n goes to infinity, where I is the indicator function.


    => this direction is easy and I have it solved.

    I wonder if anyone has any idea of how to deal with <=. Thanks.
     
    Last edited: Sep 28, 2012
  2. jcsd
  3. Sep 28, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What do you mean by I(|X| > n) ? Is it P{|X| > n}, or something else? If that is what you mean, I think the result is false: P{|X| > n}→ 0 is true for ANY random variable on ℝ, because we have P{-n ≤ X ≤ n}→ 1 as n → ∞ for any real-valued X. In order to have E |X| < ∞ you need P{|X| > n} to go to zero quickly enough. For example, the discrete random variable X with probability mass function p(n) = c/n2, n = 1,2,3, ... has E X = ∞. Note, however, that it is not necessary to have X bounded, because many familiar random variables are unbounded but have finite expectations (or even finite moments of all orders).

    RGV
     
  4. Sep 28, 2012 #3

    Mute

    User Avatar
    Homework Helper

    What is I(|X| > n)? The probability that the absolute value of X is greater than n? If that's the case, have you heard of the Cauchy distribution?

    If not, what is I(|X| > n)?
     
  5. Sep 28, 2012 #4

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook