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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?
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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.
Jun
2
comment Distribution of $\langle A,x\rangle\langle A,y\rangle + \langle B,x\rangle\langle B,y\rangle$ given $\langle x, y\rangle$
Intuitively I feel like the fact that the vectors are unit vectors, and the random rotation property of the Gaussians should be enough, but I'm not 100% sure.
Jun
2
comment Distribution of $\langle A,x\rangle\langle A,y\rangle + \langle B,x\rangle\langle B,y\rangle$ given $\langle x, y\rangle$
That would be nice, but I don't think it exists. Instead I'm just looking for what guarantees we can get with normal distributions and going to two dimensions.
Jun
2
asked Distribution of $\langle A,x\rangle\langle A,y\rangle + \langle B,x\rangle\langle B,y\rangle$ given $\langle x, y\rangle$
May
26
revised Simple $\{-1,0,1\}$ equation set
Fixed sequence names
May
26
revised Simple $\{-1,0,1\}$ equation set
added 427 characters in body
May
25
comment Simple $\{-1,0,1\}$ equation set
Well spotted! I've updated the question.
May
25
revised Simple $\{-1,0,1\}$ equation set
added 598 characters in body
May
25
asked Simple $\{-1,0,1\}$ equation set
Mar
16
revised Probability that colored balls are separated
added 1 character in body
Mar
16
answered Probability that colored balls are separated
Feb
25
accepted Probability that colored balls are separated
Feb
24
comment Probability that colored balls are separated
Something about, that in the dependent case, once you have a separated box, it increases the chance that a later box is mixed.
Feb
24
comment Probability that colored balls are separated
I suppose in the first case we don't really need to assume poisson. The main assumption is that the boxes are independent. If we use this assumption with the uniform distribution we get $((1-1/n)^r+(1-1/n)^b-(1-1/n)^{r+b})^n$. I'm sure there must be a good argument for why that's an upper bound. Just can't think of it right now.