Results 1 to 4 of 4

Math Help - E[X] and E[X^2] for function of Weibull RV

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    2

    E[X] and E[X^2] for function of Weibull RV

    I'm tryng to solve the following integrals:

    1) (x/t)*(e^(-x/t))*(1+e^(-x/t))^-2

    2) ((x^2)/t)*(e^(-x/t))*(1+e^(-x/t))^-2


    Both on negative infinity to positive infinity.

    You can see that they are both expectations of functions of a weibull random variable with theta of t and beta of 1.

    1) Y = X(1+e^(-X/t))^-2
    2) Y = (X^2)(1+e^(-X/t))^-2

    I'm not sure if you need to use that or if I just can't solve the integrals properly. Any help?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    Quote Originally Posted by dsmullan View Post
    I'm tryng to solve the following integrals:

    1) (x/t)*(e^(-x/t))*(1+e^(-x/t))^-2

    2) ((x^2)/t)*(e^(-x/t))*(1+e^(-x/t))^-2


    Both on negative infinity to positive infinity.

    You can see that they are both expectations of functions of a weibull random variable with theta of t and beta of 1.

    1) Y = X(1+e^(-X/t))^-2
    2) Y = (X^2)(1+e^(-X/t))^-2

    I'm not sure if you need to use that or if I just can't solve the integrals properly. Any help?
    See here:

    Wolfram Mathematica Online Integrator
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2010
    Posts
    2
    Quote Originally Posted by Anonymous1 View Post
    Yes, I've done that but when doing part (2), it integrates to a polylog function. I doubt that a prof would expect us to manually integrate to that so I'm wondering if I missed anything.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    There may be some slick manipulation you can use.
    You may not need it though.
    Look at the definition of polylog.
    Specifically, examine its behavior when you plug in \pm \infty.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. CDF of the Weibull Distribution
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 17th 2013, 03:06 AM
  2. Weibull distribution
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: April 17th 2013, 03:05 AM
  3. Weibull or Poisson?
    Posted in the Advanced Statistics Forum
    Replies: 12
    Last Post: March 4th 2012, 12:06 PM
  4. Exponential to Weibull
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: December 13th 2009, 11:58 PM
  5. weibull parameter
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: October 30th 2008, 02:19 PM

Search Tags


/mathhelpforum @mathhelpforum