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Central Density Function

  1. Nov 12, 2011 #1
    1. The problem statement, all variables and given/known data


    -infinity<x<infinity
    x> theta
    f(x) = [itex] \frac{\lambda}{2}e^{-\lambda (x-\theta)} [/itex]

    F(x) = [itex] \int_{-\infty}^x f(x) dx [/itex]

    2. Relevant equations



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

    [itex] \int \frac{\lambda}{2}e^{-\lambda (x-\theta)} dx [/itex]
    = [itex] -\frac{1}{2}e^{-\lambda(x-\theta)} [/itex]

    Insert the limits:
    [itex] -\frac{1}{2}e^{-\lambda(x-\theta)} + \frac{1}{2}e^{-\lambda(-\infty-\theta)} [/itex]

    = infinity.

    The last part should not be infinity so can anyone see where I go wrong?
     
    Last edited: Nov 12, 2011
  2. jcsd
  3. Nov 12, 2011 #2

    LCKurtz

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    You have defined f(x) for [itex]x>\theta[/itex]. Is it zero elsewhere? Should your lower limit be [itex]\theta[/itex]?
     
  4. Nov 12, 2011 #3
    Yes it should! Thanks

    Insert the limits:
    [itex] -\frac{1}{2}e^{-\lambda(x-\theta)} + \frac{1}{2}e^{-\lambda(\theta-\theta)} [/itex]
    =
    [itex] 1/2 -\frac{1}{2}e^{-\lambda(x-\theta)} [/itex]
     
    Last edited: Nov 12, 2011
  5. Nov 12, 2011 #4

    HallsofIvy

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    You mean [itex]e^{-\lambda(\theta- \theta)}[/itex], not [itex]e^{-\lambda(-\theta- \theta)}[/itex]
     
  6. Nov 12, 2011 #5
    Thanks, corrected it now.
     
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