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jrfawkes
08-03-2010, 08:58 PM
Itís been a while since Iíve done much probability stuff, but Iíve come across a problem in some auction theory work that Iím doing and was hoping that someone could at least point me in a fruitful direction:
Say you select a fairly small random sample (say size N) from some continuous distribution (could be normal or uniform if it would make things easier). Then you remove the n largest observations from your sample. What would be the expected value of the remaining observations?
Is this a silly question? Is there a fairly simple answer? Do I need to start delving into the world of order statistics or some such? Any help would be appreciated.

BGM
08-03-2010, 11:31 PM
Yes I guess you need to deal with the order statistic.
E.g. If your random variables are all i.i.d. uniform,
then the ordered sequence will be beta distributed.

And then you can compute the expected value of the sample mean random variable.