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Thread: Exponential (θ ) distribution question

  1. #1
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    Exponential (θ ) distribution question

    Xsub1 and Xsub2 are independent Exponential ( θ ), θ >0, random variables.

    Let S= Xsub1 +Xsub2

    Write the PDF of S stating any standard results that you use

    Find E[Xsub1 | S = s] for any given s>0

    Xsub1 is a so-called unbiased estimator of θ because E[Xsub1] = θ . Show that E[Xsub1 | S] is also an unbiased estimator of θ AND has a varience no larger than Var(Xsub1)

  2. #2
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    Re: Exponential (θ ) distribution question


    It looks like a quite standard book work. Please show some effort / narrow down the question.

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