Results 1 to 6 of 6

Math Help - sample mean question

  1. #1
    Newbie
    Joined
    Jun 2008
    Posts
    9

    sample mean question

    Y_1,Y_2, . . . ,Y_n are independent and identically distributed Exp(Q)
    random variables.
    Which are the distribution of the sample mean?

    Sample mean=X=(1/n)*SIGMA(Y_k)

    1. X~Exp(Q)
    2. X~Exp(nQ)
    3. X~Exp(Q/n)
    4. X~Gamma(n,Q)
    5. X~Gamma(n,(Q/n))

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Oct 2009
    Posts
    340
    Quote Originally Posted by MC Squidge View Post
    Y_1,Y_2, . . . ,Y_n are independent and identically distributed Exp(Q)
    random variables.
    Which are the distribution of the sample mean?

    Sample mean=X=(1/n)*SIGMA(Y_k)

    1. X~Exp(Q)
    2. X~Exp(nQ)
    3. X~Exp(Q/n)
    4. X~Gamma(n,Q)
    5. X~Gamma(n,(Q/n))

    So, what attempts have you made?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    the sum is distributed as \Gamma(n,Q) by using MGFs
    Next make a calc one change of variable to divide that rv by n.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jun 2008
    Posts
    9
    I`m sorry can you do one of them as an example I don`t quite understand.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    let W=Y_1+\cdots +Y_n

    Then by using MGFs W\sim\Gamma(n,Q)

    So, X=W/n and f_X(x)=f_W(w)\bigl|{dw\over dx}\bigr|

    SO, start by writing the density of W, which there are two ways, that's one reason I didn't
    write my gamma density.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jun 2008
    Posts
    9
    Ok thanks a lot for your help I think I`m beggining to understand it now. So 1,2,3 and 5 AREN'T distributions of the sample mean because their MGFs are different, but 4 is because its MGF is the same?

    edit; actually it`s 5 that has the same MGF as the sample mean right? not 4

    edit 2; yes i`ve definitely figured it out it`s 5 only. tell me if I`ve got it. thanks a lot for the help
    Last edited by MC Squidge; April 3rd 2011 at 02:44 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sample ODE question
    Posted in the Differential Equations Forum
    Replies: 8
    Last Post: July 8th 2010, 10:48 PM
  2. variance of sample mean and sample standard deviation
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: July 24th 2009, 06:20 AM
  3. Replies: 2
    Last Post: May 29th 2009, 10:32 AM
  4. Sample Random Sample Question 2
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: January 7th 2008, 07:58 AM
  5. Sample question
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: August 26th 2006, 06:29 PM

Search Tags


/mathhelpforum @mathhelpforum