Results 1 to 2 of 2

Math Help - Showing that Laplace distribution is a probability density

  1. #1
    Senior Member
    Joined
    Feb 2008
    Posts
    297

    Showing that Laplace distribution is a probability density

    How would you show that the laplace distribution is a probability density, i.e.

    f(x)\geq 0 and \int_{-\infty}^{\infty}f(x)dx=1

    Laplace Distribution:

    f(x)=\frac{1}{2}e^{-|x|} for -\infty<x<\infty

    Proving that f(x) \geq 0 is quite obvious

    To prove that the integral equals 1, would you consider the 2 cases where x\geq 0 and x<0? And then from that, the sum of the integrals should equal 1?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by acevipa View Post
    How would you show that the laplace distribution is a probability density, i.e.

    f(x)\geq 0 and \int_{-\infty}^{\infty}f(x)dx=1

    Laplace Distribution:

    f(x)=\frac{1}{2}e^{-|x|} for -\infty<x<\infty

    Proving that f(x) \geq 0 is quite obvious

    To prove that the integral equals 1, would you consider the 2 cases where x\geq 0 and x<0? And then from that, the sum of the integrals should equal 1?
    Yes.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. probability distribution and density function
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: January 9th 2011, 12:34 PM
  2. Probability Density of Normal Distribution
    Posted in the Statistics Forum
    Replies: 1
    Last Post: November 20th 2009, 12:50 AM
  3. Replies: 2
    Last Post: August 25th 2009, 10:39 PM
  4. beta distribution probability density function proof
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 11th 2008, 01:54 PM
  5. marginal density, conditional density, and probability
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 24th 2008, 06:50 PM

Search Tags


/mathhelpforum @mathhelpforum