Results 1 to 2 of 2

Math Help - trying (and failing) to get mean of 2 parameter exponential distribution

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    2

    trying (and failing) to get mean of 2 parameter exponential distribution

    I have the following 2 parameter exponential density function:
    a*e^(-a*[x-b]), where x>=b, a>0, neg infinity < b < pos infinity

    I start by evaluating:
    Mean = int[x*a*e^(-a*[x-b])]dx bounded by neg. and pos. infinity

    I solve the integral with integration by parts to:
    -x*e^(-a*[x-b]) - (1/a)*e^(-a*[x-b]) evaluated between neg. and pos. infinity.

    The Mean comes to be pos. infinity. If I change the lower bound the integral is evaluated over I get that the Mean is (1/a), which, I think, is the right answer. I am stumped why I can't generate (1/a) with the bounds of integration as neg. and pos. infinity. Ideas?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    let Y=X-b and this becomes the usual exponential distribution.
    the mean and variance of Y are well known and easy to compute.
    even if you wish to integrate this directly, you should use calc 1 subsitution, y=x-b.
    AND the lower bound of x is b in your integral.
    You need to show your work.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Let X have a Poisson distribution with parameter...
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 11th 2010, 04:04 PM
  2. Replies: 1
    Last Post: November 23rd 2009, 10:57 AM
  3. exponential distrib with 1/gamma parameter
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 31st 2009, 09:34 AM
  4. Exponential distribution with an unknown parameter, theta
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: April 29th 2009, 04:21 PM
  5. one-parameter weibull distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 4th 2008, 08:16 PM

Search Tags


/mathhelpforum @mathhelpforum