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Sufficient statistics

  1. Jan 18, 2013 #1
    1. The problem statement, all variables and given/known data
    Problem is in the attachment, sorry, I can't figure out how to do tex in this message board system.


    2. Relevant equations



    3. The attempt at a solution
    In the attachment.
     

    Attached Files:

  2. jcsd
  3. Jan 19, 2013 #2
    I think you're into too much math. The I(.) function, if I get its meaning correctly, is nothing but to indicate that it is impossible to sample [itex]x\leq\mu[/itex]. With frequentists' approach, this means a lot: you can safely ignore the bunch of I(.)'s and consider only those samples greater than [itex]\mu[/itex]. This should solve the problem :wink:
     
  4. Jan 19, 2013 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    Ignoring the fancy notation, what you have for given, fixed μ is that Y = X-μ is exponentially distributed with unknown mean, and you are trying to estimate that mean. You are being asked to show some property of the "usual" estimate.
     
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