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Math Help - exponential random variable with a random mean?

  1. #1
    frm
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    exponential random variable with a random mean?

    Hi all,
    I'm wondering how could I model a r.v. B which is exponentially distributed (i.e. with pdf f(b)=kexp(-kb)u(b) with u(b) = the step function) but whose parameter k is itself a random variable, not a fixed deterministic value.

    Since:
    f(b|k)=f(b,k)/f(k)
    I think I can write:
    f(b,k)=f(b|k)f(k)=kexp(-kb)u(b)f(k)
    is this correct?

    Thanks!
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  2. #2
    Moo
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    Hello,

    You don't know whether k has a pdf or not. So it's not really correct to write f(k). If you assume so, it's ok.
    And your whole formula is ok (actually, u(b)=1 iff b>0)
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  3. #3
    frm
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    Hi,
    I assume that k is a r.v. so as you say everything is ok.

    Thanks for confirming it!
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