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Homework Help: Finding PDF of uniform distribution

  1. May 5, 2010 #1
    1. The problem statement, all variables and given/known data

    Let X be a uniform random variable in the interval [0,1] i.e., X = U [(0,1)]. Then a new random variable Y is given by Y= g(X), where g(x)= -a. ln(x). Show that Y is exponentially distributed. What is the mean of Y?



    2. Relevant equations

    fX(x) = 1/ lambda . exp (-x/ lambda)

    0 otherwise


    3. The attempt at a solution

    Y = g(X) can be computed via FY(y)= Summation 1/ differentiation of g(x) multiplied with Fx(x)
    I can't show how this is exponential.

    Please help!
     
  2. jcsd
  3. May 5, 2010 #2

    lanedance

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    Homework Helper

    so as its constant doesn't [itex]f_X(x)=1[/itex] in [0,1], zero otherwise

    then use the fact that the probabilty for a given interval dx and corresponding interval dy must be the same
    [tex] |f_X(x)dx| = |f_Y(y)dy| [/tex]
     
  4. May 5, 2010 #3

    lanedance

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    Homework Helper

    is that what you tried to do? can you show your working?
     
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