Results 1 to 5 of 5

Math Help - Expected value of a complicated density function

  1. #1
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2

    Expected value of a complicated density function

    Let X be a randon variable with density function:

     f(x) = \frac {cx^6}{1+7x^{20}} \ \ \ \ \ -1 \leq x \leq 1

    and  f(x) = 0 \ \ \ otherwise

    where c is such that this is a density.

    Find E[X]

    First I tried to take the integral of  \int _{-1}^{1} \frac {cx^6}{1+7x^{20}} = 1 to find c, but I'm stuck here unless I get to use a calculator.

    Are there anyway to find c? Or rather, do I need to find c in order to find the expected value, that is,  \int _{-1}^{1} \frac {cx^7}{1+7x^{20}}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Nov 2009
    Posts
    34
    Use partial fractions to integrate?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    Why being complicated ?

    E(X)=\int_{-1}^1 \frac{cx^7}{1+7x^{20}} ~dx

    since we integrate an odd function over a symmetric interval over 0, the integral is 0 !


    More generally, if the pdf of a rv is an even function, then all the odd moments of the rv are 0
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Moo View Post
    Hello,

    Why being complicated ?

    E(X)=\int_{-1}^1 \frac{cx^7}{1+7x^{20}} ~dx

    since we integrate an odd function over a symmetric interval over 0, the integral is 0 !


    More generally, if the pdf of a rv is an even function, then all the odd moments of the rv are 0
    There's a restriction required on this statement (otherwise what are we to make of the Cauchy Distribution ....?)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Oh, indeed !
    Then if the moment exists... which is okay here since there's a continuous function in a compact.

    So it doesn't work for the Cauchy distribution because the x*pdf near infinity is equivalent to 1/x, which is not integrable.

    (hey I hate justifying things like that ^^)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Joint Probability Density Function/Finding expected Value
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 5th 2011, 02:23 PM
  2. Joint Density Expected Value
    Posted in the Statistics Forum
    Replies: 5
    Last Post: November 8th 2011, 11:28 AM
  3. Joint Density expected values
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: September 5th 2011, 12:32 AM
  4. Minimizing the expected value of a density function
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 16th 2010, 11:28 PM
  5. Distribution to density to expected
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: April 24th 2008, 12:07 AM

Search Tags


/mathhelpforum @mathhelpforum