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seen Aug 7 '13 at 5:49

Aug
7
comment A problem on a proof in a graph theory textbook
I see. "shortest" is the key. Thank you very much!
Jul
27
comment How to prove connectivity $\leq$ minimum degree?
Thanks. Seem we have different definition of connectivity, but yours seems better for this question.
May
6
comment Relation about Gateaux differentiable and differentiable
differentiable is what we meet in undergraduate calculus course (see, e.g., Def. 9.11 in P212 of baby Rudin). Gateaux differentiable (at x) is defined as follows: (1)the directional derivative $f'(x;v)$ exists for all $v\in\mathbb{R}^n$, (2)there exists (unique) $f_G'(x)\in\mathbb{R}^*$ such that $f'(x;v)=<f_G'(x),v>$ for all $v\in\mathbb{R}^n$, where $\mathbb{R}^*$ means the dual space of $\mathbb{R}^n$.
May
5
comment Relation about Gateaux differentiable and differentiable
Thank you!_____
May
4
comment A question about definition of hyperplane
Thank you......
Mar
16
comment Ask for a question about independence
I answered my question, but I would like to give the credit to you.
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
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
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:-(
Feb
21
comment An optimization problem with regard to permutation function
I got it. Thank you! (I mean the former)
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
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
16
comment A question about independence wrt joint random variable
Thank you. I worked it out. We have now $p(x|y_1y_2)=p(x)$. So $p(x|y_1)=\frac{p(xy_1)}{p(y_1)}=\frac{\sum\limits_{y_2}p(xy_1y_2)}{p(y_1)}$$=\f‌​rac{\sum\limits_{y_2}p(x|y_1y_2)p(y_1y_2)}{p(y_1)}=\frac{\sum\limits_{y_2}p(x)p(y‌​_1y_2)}{p(y_1)}=\frac{p(x)\sum\limits_{y_2}p(y_1y_2)}{p(y_1)}=\frac{p(x)p(y_1)}{p‌​(y_1)}=p(x)$. So 2) is true. Thank you again.
Feb
16
comment A question about independence wrt joint random variable
Thank you. So 1) is not true. What about 2)?
Jan
22
comment Ask for a proof of an upper bound
Thank you!_____
Jan
22
comment Ask for a proof of an upper bound
wonderful!______
Jan
20
comment limit of probability
Using the same method Mercy gave, we can prove that $P(A_n\cup B_n)\to 1$.