Central Density Function

  • Thread starter MaxManus
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  • #1
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Homework Statement




-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]

Homework Equations





The Attempt at a Solution


Homework Statement



[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:

Answers and Replies

  • #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]?
 
  • #3
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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:
  • #4
HallsofIvy
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You mean [itex]e^{-\lambda(\theta- \theta)}[/itex], not [itex]e^{-\lambda(-\theta- \theta)}[/itex]
 
  • #5
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Thanks, corrected it now.
 

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