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Aug
17
comment Upper bounding a tricky sum
Great thinking splitting the sum up by cases like that! I learned a lot from studying this answer.
Aug
17
accepted Upper bounding a tricky sum
Aug
15
comment Upper bounding a tricky sum
@AndrásSalamon Ah, I hadn't tried that! I don't think I can entirely discard $d$, but $(1-x)^n\le1/(1+nx)$ seems to work very well. Except it doesn't let me evaluate the sum..
Aug
15
comment Upper bounding a tricky sum
@AndrásSalamon The best upper bound I can get is $1$.
Aug
15
comment Upper bounding a tricky sum
@PaulSinclair you are right, I'd like to find the smallest $m$ necessary, like $m= 2^k/p$ or so, to make the sum go to 0 as $k\rightarrow \infty$.
Aug
15
revised Upper bounding a tricky sum
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Aug
15
revised Upper bounding a tricky sum
added 53 characters in body
Aug
15
revised Upper bounding a tricky sum
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Aug
15
asked Upper bounding a tricky sum
Aug
4
awarded  Popular Question
Jul
15
comment Is conditional entropy ever taken to be a random variable?
Yes, which is similar to the classical definition of conditional expectation. However you see how it could instead be defined similar to the modern definition of conditional expectation, and thus be a random variable?
Jul
15
comment Is conditional entropy ever taken to be a random variable?
Yes, what I wonder about is if there are any cases in which it makes sense to use it as a random variable, similar to conditional expectation? And if there is an intuitive reason why this is not usually done?
Jul
15
asked Is conditional entropy ever taken to be a random variable?
Jun
11
comment Integral of 2D Gaussian over triangle
For my case I got a reasonably good result by plugging in an approximation to $erf(x)\approx 1-e^{-\frac{2 x \left(x+\sqrt{\pi }\right)}{\pi }}$ in the integral you describe.
Jun
10
comment A.M.>G.M. of four numbers
I don't think your expansion is correct. You need to divide everything by $4^4$.
Jun
8
comment Calculate the area on a sphere of the intersection of two spherical caps
If a future reader is interested in this problem for high dimensional spaces, consider having a look at ie.kaist.ac.kr/isyse/professor/tech_file/…
Jun
3
revised What is the expectation of $ X^2$ where $ X$ is distributed normally?
Link for easy browsing
Jun
3
suggested approved edit on What is the expectation of $ X^2$ where $ X$ is distributed normally?
Jun
3
comment Distribution of $\langle A,x\rangle\langle A,y\rangle + \langle B,x\rangle\langle B,y\rangle$ given $\langle x, y\rangle$
Basically if you expand the expression you get the grand sum of $(AA^T+BB^T)\odot xy^T$. If the elements of $A$ and $B$ are zero in expectation, so are all the non diagonal elements of $AA^T$ and $BB^T$, but not the diagonals. Hence only the diagonal of $xy^T$ survives, which is $\langle x,y\rangle$.
Jun
3
comment Distribution of $\langle A,x\rangle\langle A,y\rangle + \langle B,x\rangle\langle B,y\rangle$ given $\langle x, y\rangle$
Also, it works in expectation, where you get $n\sqrt{2/\pi}\langle x,y\rangle$, $n$ being the number of dimensions you reduce to. Maybe I can just use an AMS sketch then.