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Mar
6
comment Independence of valuations
Here's how I show $\mathfrak{p}=x_iA$.After Arturo Magidin's remark, clearly what we need to show is $x_iR_i\cap A\subset x_iA$. Take $y\in x_iR_i\cap A$. Then $y=x_i r_i$ for some $r_i\in R_i$. On the other hand, since $x_i$ is not in $\mathfrak{p}_j$,$j\neq i$, it has an inverse $x_{ij}'$ in each $R_j$. So $r_i=x_{ij}'y\in R_j$, so $r_i\in A$. Done.
Mar
6
revised Independence of valuations
name book and a typo
Mar
6
suggested suggested edit on Independence of valuations
Mar
3
awarded  Commentator
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
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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
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Feb
24
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Feb
19
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Feb
19
accepted What conic curve is the graph of y=sin(x) from 0 to pi?