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 Mar 3 comment Does exceptionalism persist as sample size gets large? @Shai, Yes I agree your result is correct. They take $X_{n,n}$ as minimum, so the order is decreasing. I also take back my comment that the difference goes to 0; in fact for exponential with parameter 1, it goes to 1. However, there must be a relation between the pdf and that limit. Mar 3 comment Does exceptionalism persist as sample size gets large? @Shai, you can see it also here: jstor.org/pss/2332028 Mar 3 comment Does exceptionalism persist as sample size gets large? "Expected values of normal order statistics", Biometrika, 48 Mar 3 comment Does exceptionalism persist as sample size gets large? What I found is that $${\rm E}[X_{r + 1:n} - X_{r:n} ] = {n \choose r}\int_{ - \infty }^\infty {[1-F(x)]^r [F(x)]^{n - r}\, dx} ,\;\; r = 1, \ldots ,n - 1.$$ If the pdf is symmetric, such as normal, it wouldn't matter, but if the pdf is not symmetric, it matters. I think the difference between the largest and the second largest goes to 0 when n increases for any continuous real distribution. Intuitively, it makes sense. Mar 1 comment Discrete maths fundamentals Possible duplicate:math.stackexchange.com/questions/1533/… and math.stackexchange.com/questions/350/… Mar 1 answered Prove that two any consecutive terms of Fibonacci sequence are relatively prime Mar 1 revised Help understanding tensoring of exact sequences added 1 characters in body Mar 1 awarded Editor Mar 1 comment Help understanding tensoring of exact sequences Thanks. I modified it. Mar 1 revised Help understanding tensoring of exact sequences deleted 39 characters in body; added 1 characters in body Mar 1 answered Help understanding tensoring of exact sequences Feb 27 awarded Supporter Feb 27 awarded Teacher Feb 24 awarded Quorum Feb 19 awarded Scholar Feb 19 accepted What conic curve is the graph of y=sin(x) from 0 to pi? Feb 19 awarded Student Feb 19 asked What conic curve is the graph of y=sin(x) from 0 to pi?