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Probability: Determining the distribution and range of a random variable

  1. Apr 24, 2010 #1
    1. The problem statement, all variables and given/known data

    The RV X has parameter p>0 and distribution:

    fX(x) = pxe-px for x [tex]\geq[/tex] 0 and is 0 otherwise

    (The subscript X is a capital letter, as is the X mentioned below in the e4X)

    If we are to consider the RV D= e4X, determine the range and distribution fD(d)

    2. Relevant equations

    3. The attempt at a solution

    I found this question as an exercise in a textbook, but do not know how to answer it!
    Does anyone have any suggestions that I can try out please?
  2. jcsd
  3. Apr 24, 2010 #2


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    Start by figuring out what p must be for fX to be a density function.

    If D = e4X, one way to get at its density function is to use the cumulative distribution:

    P(D ≤ d) = P(e4X ≤ d) = P(4X ≤ ln(d)) = P( X ≤ (1/4)ln(d) )

    Presumably you can calculate that, which will give you the cumulative distribution function for D. Differentiate to get fD(d).
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