Results 1 to 3 of 3

Math Help - Central limit theorem

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    21

    Central limit theorem


    Hi i need some help with the question below, struggling to know how to apply the central limit theorem,

    The Xi are a sequence of independent identical random variable with the given distrabution below

    thanks for any help
    Attached Thumbnails Attached Thumbnails Central limit theorem-question.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    First obtain the CDF of the max of your sample.

    Let Y_n=max\{X_1,\ldots X_n\}

    F_{Y_n} =\biggl(F_{X_i}(x)\biggr)^n=\biggl({x\over\theta}\  biggr)^n

    So P(n(\theta-Y_n)\le x) =1-P\biggl(Y_n\le \theta -{x\over n}\biggr)=1-\biggl(1-{x\over\theta n}\biggr)^n

    \to 1-e^{-x/\theta}

    and why do you think the CLT is involved here?
    Not all convergences in distribution are to a normal.
    Plus we're not observing a sum here either.
    Last edited by matheagle; January 3rd 2010 at 09:59 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2009
    Posts
    21
    question before involved CLT, was being a fool

    thanks for you help
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Central limit theorem
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: May 15th 2011, 09:17 AM
  2. Central Limit Theorem
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: March 8th 2011, 05:05 PM
  3. Central Limit Theorem
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: June 17th 2009, 10:27 PM
  4. Central Limit Theorem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 12th 2008, 01:04 PM
  5. central limit theorem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 31st 2008, 04:31 PM

Search Tags


/mathhelpforum @mathhelpforum