Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By abender

Math Help - help with exponential distribution question

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    london
    Posts
    16

    help with exponential distribution question

    The lifetime of a certain component may be modelled by the exponential distribution with a probability density function f(t) = lambda * e^(-lambda*t).

    Show that for this distribution P(T>t) = e^(-lambda*t)?

    Any help would be very appreciated!!

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Mar 2008
    From
    Pennsylvania, USA
    Posts
    269
    Thanks
    37

    Re: help with exponential distribution question

    f_T(t) = \lambda e^{-\lambda t}, t>0

    F_T(t) = \int^{x=t}_{x=0}\lambda e^{-\lambda x}dx = \frac{\lambda e^{-\lambda x}}{-\lambda}|^{x=t}_{x=0}  = -e^{-\lambda x}|^{x=t}_{x=0} = e^{-\lambda x}|^{x=0}_{x=t} =  1 - e^{-\lambda t}

    P(T>t) = 1 - F_T(t) = 1 - \left(1 - e^{-\lambda t}\right) = e^{-\lambda t}
    Thanks from JDAWES
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2013
    From
    london
    Posts
    16

    Re: help with exponential distribution question

    this follows on from the previous question;

    In a test n items were used, m items failed, having times to failure t1, t2,...tm.
    The remaining items were still working when the test was terminated at time t0.

    Show the maximum likelihood estimate for lambda is m/ ((sum of t i) +(n-m)*t0)?

    I'v been doing this question and iv got up to the point where you need to substitute in the test: the likelihood is n/sum of ti but dont know how to do the rest?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exponential Distribution Question
    Posted in the Statistics Forum
    Replies: 5
    Last Post: November 5th 2011, 02:20 AM
  2. Exponential Distribution question
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: July 9th 2010, 10:22 PM
  3. Exponential Distribution Question
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: October 28th 2009, 12:04 PM
  4. exponential distribution question
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: September 23rd 2008, 12:15 AM
  5. exponential distribution question
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: September 6th 2008, 06:46 PM

Search Tags


/mathhelpforum @mathhelpforum