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If an exponential random variable, X, has failure rate λ, what is E[X|X<λ]?

I'm not sure how to start here. I know that E[X] = 1 / λ for an exponential random variable. Is the probability that X < λ = 1-e^(-λ*λ)?

Can I use this identity E[X] = E[X|X < c]P{X < c} + E[X|X > c]P{X > c}?

  • ... or Cross Validated (http://stats.stackexchange.com/). – David G. Stork May 20 '15 at 20:58
  • As others have stated, you've posted this question on the wrong site. However, for fun, here's how you could compute this in Mathematica: Expectation[x \[Conditioned] x < \[Lambda], x \[Distributed] ExponentialDistribution[\[Lambda]]] –  May 20 '15 at 21:00
  • @DavidG.Stork Regarding that point, when flagging the post for migration I realized that I can only suggest math or meta as alternative sites. Actually, I have been seeing quite a few questions that would fit on Cross Validated better than math. Do you (or does anybody) know how to suggest another alternative site? –  May 20 '15 at 21:00
  • Oh, I apologize. I'll post it to math.stackexchange. –  May 20 '15 at 21:01
  • @MarcoB Searching our Meta site, you will find discussions of this very topic, but they have not gone anywhere. – bbgodfrey May 20 '15 at 21:06
  • @bbgodfrey Thank you for the pointer, I'll have a look. –  May 20 '15 at 21:09
  • @MarcoB I don't fully understand the constraints on suggested migration sites, but perhaps I can flag a post for migration to Mathematics and to Cross validated because I'm a member of these and have a reputation on each. – David G. Stork May 20 '15 at 22:37

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