Results 1 to 2 of 2

Math Help - Problem utilizing order statistics

  1. #1
    Newbie
    Joined
    Jan 2011
    Posts
    9

    Problem utilizing order statistics

    Hello all. The problem statement is as follows:

    Consider a system containing n components where the lifetimes of the compoenets are independent random variables and each has pdf f_y(y) = λe^(-λy), y > 0. Show that the average time elapsing before the first component failure occurs is 1/nλ

    I'm not really sure where to go with this problem. I feel that I should first find the pdf of the order statistic Y_(1), but I'm not sure where to go after that. Any help is appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jmyers12345 View Post
    Hello all. The problem statement is as follows:

    Consider a system containing n components where the lifetimes of the compoenets are independent random variables and each has pdf f_y(y) = λe^(-λy), y > 0. Show that the average time elapsing before the first component failure occurs is 1/nλ

    I'm not really sure where to go with this problem. I feel that I should first find the pdf of the order statistic Y_(1), but I'm not sure where to go after that. Any help is appreciated.
    Calculate the pdf of W = Y_{(1)} and use it to calculate the mean of W.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. order statistics
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: July 11th 2010, 09:19 AM
  2. Order statistics
    Posted in the Advanced Statistics Forum
    Replies: 10
    Last Post: April 4th 2010, 12:43 PM
  3. A word problem utilizing matrices.
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: March 15th 2010, 12:03 AM
  4. Proof utilizing archemedian principle
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 1st 2010, 05:52 PM
  5. Order statistics problem
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 21st 2009, 09:02 AM

Search Tags


/mathhelpforum @mathhelpforum