Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Conditional expectation of Exp(theta)

  1. Nov 30, 2009 #1
    Given X follows an exponential distribution [tex]\theta[/tex]

    how could i show something like

    [tex]\operatorname{E}(X|X \geq \tau)=\tau+\frac 1 \theta[/tex]


    i have get the idea of using Memorylessness property here,
    but how can i combine the probabilty with the expectation?


  2. jcsd
  3. Nov 30, 2009 #2
    If you write down mathematically the Memorynessless property then it might become obvious. Otherwise it's fine to express the conditional expectation as a ratio of integrals and evaluate it directly.
  4. Dec 1, 2009 #3
    [tex]\Pr(T > s + t\; |\; T > s) = \Pr(T > t) \;\; \hbox{for all}\ s, t \ge 0. [/tex]

    i just cant convert from expectation to the probability...

  5. Dec 5, 2009 #4
    That's what I did so far.

    But I just cant use the memoryless property to do it ....

    http://img138.imageshack.us/img138/5945/tempz.jpg [Broken]

    Attached Files:

    • temp.jpg
      File size:
      26.2 KB
    Last edited by a moderator: May 4, 2017
  6. Dec 6, 2009 #5
    Hint: rewrite the memoryless property into a form suitable to use on line 1 of your proof. Conditional probabilities -> conditional cdf -> conditional pdf.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook