Results 1 to 2 of 2

Math Help - Normalization Constant

  1. #1
    Junior Member
    Joined
    Nov 2006
    Posts
    41

    Normalization Constant

    Calculate normilization constant for f(x) = e^ [1.5(x^2)]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by myoplex11 View Post
    Calculate normilization constant for f(x) = e^ [1.5(x^2)]
    I think you mean e^{-1.5x^2} because the former does not convergene when we take the integral.

    We need to find a constant ("normalization") k so that:
    k\int_{-\infty}^{\infty} e^{-1.5x^2} dx = 1
    In order to turn it into a probability density function.

    Thus,
    k\int_{-\infty}^{\infty} e^{-(\sqrt{1.5} x)^2} dx = 1
    Let t=\sqrt{1.5}x use this substitution to get,
    \frac{k}{\sqrt{1.5}}\int_{-\infty}^{\infty} e^{-t^2} dt = 1
    Thus,
    k \cdot \sqrt{1.5}^{-1} \cdot \sqrt{\pi} = 1
    Thus,
    k = \frac{\sqrt{3}}{\sqrt{2\pi}}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Normalization
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: July 4th 2011, 11:33 PM
  2. Replies: 0
    Last Post: May 4th 2010, 09:38 AM
  3. Normalization
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 30th 2009, 08:36 PM
  4. Normalization constant
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: February 23rd 2009, 07:02 AM
  5. Replies: 5
    Last Post: February 29th 2008, 03:05 PM

Search Tags


/mathhelpforum @mathhelpforum