Results 1 to 4 of 4

Math Help - question about a "half normal" distribution? Thanks for checking this out.

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    69

    Red face question about a "half normal" distribution? Thanks for checking this out.

    Let X be N (0, 1)

    (a) How do you find the p.d.f of |X|, a distribution that is often called the half normal?

    (b) How do you find the expectation of |X| ?

    Thank you for your time.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Focus's Avatar
    Joined
    Aug 2009
    Posts
    228
    Quote Originally Posted by Intsecxtanx View Post
    Let X be N (0, 1)

    (a) How do you find the p.d.f of |X|, a distribution that is often called the half normal?

    (b) How do you find the expectation of |X| ?

    Thank you for your time.
    Hint: \mathbb{P}(|X| =a)=\mathbb{P}(X=a)+\mathbb{P}(X=-a) if a\geq 0 and zero otherwise.

    Second hint: Normals are symmetric about their mean.

    After you find the pdf integrate to find the expectation. If you need help with that, post here.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Oct 2009
    Posts
    340
    Well, P(|X| = a) is zero for all a. But,  F_{|X|} (x) = P(|X| \le x) = P(-x \le X \le x) = F_X (x) - F_X (-x), which is enough to get the pdf by taking the derivative WRT x (note that, up to this point and after taking the derivative, we haven't used any information about the distribution of X). To find the expectation, just for simplicity let's set Y = |X| then find the expectation of Y in the usual way, now that we have the pdf for it. The function you need to integrate has an easy enough antiderivative.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Oct 2009
    Posts
    195


    Who is this btw?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: October 17th 2011, 02:50 PM
  2. Replies: 1
    Last Post: September 16th 2011, 01:08 AM
  3. Replies: 2
    Last Post: April 24th 2011, 07:01 AM
  4. Replies: 1
    Last Post: October 25th 2010, 04:45 AM
  5. Replies: 1
    Last Post: June 4th 2010, 10:26 PM

Search Tags


/mathhelpforum @mathhelpforum