Conditional expectation of exponential distribution.

  • Thread starter manish13
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  • #1
manish13
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I have been stuck at this calculation. There are two exponential distributions X and Y with mean 6 and 3 respectively. We need to find
E[y-x|y>x]
I keep getting it negative, which is clearly wrong. Anybody wants to try it?
 

Answers and Replies

  • #2
mathman
Science Advisor
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Show your calculation. It should be easy to find the flaw.
 
  • #3
manish13
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I got it finally. But here is a brief note about it

[tex]E[t_2-t_1|t_2>t_1] = E[(t_2-t_1)*I_{\{t_2>t_1\}}] = \int_0^{\infty} \int_{t_1}^{\infty}(t_2-t_1)\lambda_1 \lambda_2 e^{-\lambda_1 t_1} e^{-\lambda_2 t_2} dt_2 dt_1[/tex]

This nicely gives the answer as [tex]\frac{\lambda_1}{\lambda_2(\lambda_1+\lambda_2)}[/tex]

I was doing a mistake in byparts.
 

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