Point Estimation problem - when variance of MLE attains CRLB?

Discussion in 'CT3' started by Chandrima, Feb 3, 2017.

  1. Chandrima

    Chandrima Member

    Dear sir/ma'm,
    Please find the following question attached herewith (in picture link provided). I could proceed upto part (iii) and got CRLB as lambda^2/n. But i could not do part (iv) to show that variance of lambda-cap equals CRLB. How to do it? If I proceed like this variance(lambda-cap) = E(lambda-cap^2) - [E(lambda-cap)]^2 then I am getting both E(lambda-cap^2) = lambda^2 as well as E(lambda-cap) is also lambda. So both are cancelling out to give variance(lambda-cap) as zero. I feel what I am doing is wrong. Someone please help to solve me part (iv).

    The photo can be found in below link

    https://drive.google.com/file/d/0B_djFkkm9kUfV3dBb3N6YXVGb3c/view?usp=drivesdk

    (please message me if the photo is not visible)
     
    Last edited by a moderator: Feb 4, 2017
  2. Bharti Singla

    Bharti Singla Senior Member

    Photo is not visible.
     
  3. Chandrima

    Chandrima Member

    Can you kindly check now?
     
  4. Bharti Singla

    Bharti Singla Senior Member

    Using Lembda cap= (summation of Xi)/n
    from part (i), i.e. MLE
     

    Attached Files:

  5. Chandrima

    Chandrima Member

    Thank you a lot Bharti ma'm!
     
  6. Bharti Singla

    Bharti Singla Senior Member

    Pleasure!! :)
     

Share This Page