Results 1 to 5 of 5

Math Help - A question about PDF of Uniform Distribution

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    10

    A question about PDF of Uniform Distribution

    Hi, this is probably ultra trivial, but here it goes

    We know that \int_{-\infty }^{\infty}f(x)dx=\int_{-\infty}^{c}f(x)dx+\int_{c}^{\infty}f(x)dx , where \int_{-\infty}^{c}f(x)dx=\lim_{a->-\infty}\int_{a}^{c}f(x)dx etc.

    Now pdf for uniform dist is defined as:

    f(x)=\left\{\begin{matrix}<br />
\frac{1}{b-a}\: \! ( \: a\leq x\leq b)\\<br />
0 \;  (x>b \; or \; x<  <br />
a)<br />
\end{matrix}\right.
    so I apply the above formula, which yields 1+1 = 2

    i.e. \lim_{a->-\infty}\int_{a}^{c}f(x)dx = \lim_{a->-\infty}\left ( \frac{c-a}{b-a} \right )= (L'Hopital)\lim_{a->-\infty}\left ( \frac{1}{1} \right )=1
    and similarly 1 for the other one as well.

    But all the probability books I'm checking says that \int_{-\infty }^{\infty}f(x)dx=1
    Can anybody explain me what am I doing wrong?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,661
    Thanks
    1616
    Awards
    1
    Quote Originally Posted by ichoosetonotchoosetochoos View Post
    f(x)=\left\{\begin{matrix}<br />
\frac{1}{b-a}\: \! ( \: a\leq x\leq b)\\<br />
0 \;  (x>b \; or \; x<  <br />
a)<br />
\end{matrix}\right.
    \int_{-\infty }^{\infty}f(x)dx=1
    Evaluate \int_{ - \infty }^a {f(x)dx}  + \int_a^b {f(x)dx}  + \int_b^\infty  {f(x)dx}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    Posts
    10
    ok that was quite a dumb question, got it now
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2010
    Posts
    10
    this rests on the assumption that a is bigger than minus infinity and b is smaller than infinity though
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,661
    Thanks
    1616
    Awards
    1
    Quote Originally Posted by ichoosetonotchoosetochoos View Post
    this rests on the assumption that a is bigger than minus infinity and b is smaller than infinity though
    Look at the definition of uniform distribution very carefully.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Continuous uniform distribution question
    Posted in the Statistics Forum
    Replies: 2
    Last Post: August 27th 2011, 03:03 PM
  2. [SOLVED] Mixing a uniform distribution with a normal distribution
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: July 8th 2011, 08:27 AM
  3. Uniform Distribution question
    Posted in the Advanced Statistics Forum
    Replies: 9
    Last Post: May 16th 2011, 10:21 AM
  4. Uniform Distribution Question
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 18th 2009, 03:34 PM
  5. [SOLVED] Uniform Distribution Question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 10th 2007, 06:53 AM

Search Tags


/mathhelpforum @mathhelpforum