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seen Aug 7 '13 at 5:49

Mar
16
answered Ask for a question about independence
Mar
6
accepted Ask for a thing about multivariable concave function
Mar
6
comment Ask for a thing about multivariable concave function
Great! So, is sufficiently smooth concave function a special case of Lipschitz continuous function?
Mar
6
revised Ask for a thing about multivariable concave function
added 22 characters in body
Mar
6
comment Ask for a thing about multivariable concave function
I see the mistake in the post. I should add "absolute value of"
Mar
6
comment Ask for a thing about multivariable concave function
why $M$ does not exist for $-x^2$? It is a convex function and the slope of the tangent line on the parabola satisfies the inequality for the fixed $x_0$ and all other $x$.
Mar
6
comment Ask for a thing about multivariable concave function
why not M=1? you know what I mean. And, if we take M=17, the inequality does not hold for all x.
Mar
6
asked Ask for a thing about multivariable concave function
Mar
4
accepted Expression for the size of type class, or multinomial coefficient.
Mar
3
answered Expression for the size of type class, or multinomial coefficient.
Mar
2
comment Expression for the size of type class, or multinomial coefficient.
It seems that we can use Stirling's approximation $n!\approx\sqrt{2\pi n}(n/e)^n$. But this is only an approximation and a big-O term $O(\ldots(n))$ or something is needed for the equation to hold exactly. I don't know what form of $O(\ldots(n))$ is. Any comment is welcome! ... I have to go to bed now:-(
Mar
2
asked Expression for the size of type class, or multinomial coefficient.
Feb
21
accepted An optimization problem with regard to permutation function
Feb
21
comment An optimization problem with regard to permutation function
I got it. Thank you! (I mean the former)
Feb
21
asked An optimization problem with regard to permutation function
Feb
17
comment Ask for a question about independence
@Did: so the independence of $X'$ and $(X,Y)$ can not be derived from the independence of $X$ and $X'$? Note that $Y$ is generated solely from $X$, not like $Y=X+X'$ in the answer where $Y$ is also determined by $X'$.
Feb
17
comment Ask for a question about independence
Yes, I must have omitted some assumptions, but I don't know what they are. Currently the assumptions can be summarized as: $X$ and $X'$ are iid with common probability $p(x)$. $Y$ is generated from $X$ according to the trasition probability $p(y|x)$ (sorry for the typo in the original post; I have corrected it). I really can not think of any other assumptions. Maybe someone who read the proof of Shannon's channel coding theorem before and familiar with random coding and joint typicality can answer this question.
Feb
17
revised Ask for a question about independence
edited body
Feb
17
comment Ask for a question about independence
but $X'$ and $Y$ are indeed independent in the proof to show subsequent results. Let's assume $X'$ and $X$ have the same distribution.
Feb
17
asked Ask for a question about independence