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Im exp(-rm)

  1. Jun 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Assuming 'm' is deterministic the probability distribution of a Random Variable(R.V) r is f(r)=m exp(-rm) Now m itself is a another R.V with a probability distribution g(m). Is it correct to say that now the probability distribution of 'r' is f(r)=E_m [m exp(-rm)] where E_m is the statistical expectation operation with respect to 'm'. If it is correct can some one give me a mathematical reference (some journal publications or book)?


    2. Relevant equations

    f(r)=m exp(-rm)

    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 20, 2009 #2

    Redbelly98

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    That doesn't look right. The final f(r), after accounting for the distribution of m's, should not depend on m.

    I think you need to weight the first f(r) (the one that does depend on m) by g(m), then integrate that over m to get the final f(r).
     
  4. Jun 20, 2009 #3
    Thanks a lot for your reply. I agree with you that the final f(r), after accounting for the distribution of m, should not depend on m. Now shall i follow these steps

    1. First find f(r) as a function of r and m where m is a random variable with the distribution g(m).
    After that
    2. Now int_{range of m}f(r)g(m)dm to get rid of m and find the final expression for f(r)

    Are these steps correct?
     
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