Q&A Bank Part 2: Qn 2.6

Discussion in 'CT6' started by jm_kinuthia, Jun 27, 2013.

  1. jm_kinuthia

    jm_kinuthia Member

    Someone please explain to me why E(Xbar)=E(Xj).
     
    jm_kinuthia, Jun 27, 2013
    #1
  2. jm_kinuthia

    jm_kinuthia Member

    Tutors ? Anyone to help ?
     
    jm_kinuthia, Jun 28, 2013
    #2
  3. suraj

    suraj Member

    I think this is because sample mean is an unbiased estimator of population mean.
     
    Last edited by a moderator: Jun 29, 2013
    suraj, Jun 29, 2013
    #3
  4. JRB1304

    JRB1304 Member

    I think there's a simpler explaination. Since each Xj are identically distributed, each expected value of Xj is Xbar.
     
    Last edited by a moderator: Jun 29, 2013
    JRB1304, Jun 29, 2013
    #4
  5. John Lee

    John Lee ActEd Tutor Staff Member

    Apologies for the delay.

    Tey are all identical and have the same mean.

    In addition the sample mean is an unbiased estimator of the mean (See Chapter 10 of CT3) so it will be the same as the mean of any one of the \( X_j 's \)
     
    John Lee, Jul 2, 2013
    #5
  6. jm_kinuthia

    jm_kinuthia Member

    Thanks all.

    Makes sense now.
     
    jm_kinuthia, Jul 8, 2013
    #6

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