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Sep
2
answered CDF calculation
Aug
22
revised Should I throw the dice again if I have rolled 4?
added 100 characters in body
Aug
22
answered Should I throw the dice again if I have rolled 4?
Jul
1
comment Where can I find an ontology of algebraic structures?
I mean "deep" in the sense of "thorough", not "profound". My Abelian Variety graph isn't thorough at all.
Jul
1
comment Subgroup of roots of unity of a field.
that's really overkill, checking group axioms takes 10 seconds
Jul
1
revised Where can I find an ontology of algebraic structures?
added 232 characters in body
Jul
1
comment Where can I find an ontology of algebraic structures?
I provided a link that describes what I mean by ontology. These two Wikipedia article are a good start, but I'm looking for something much deeper. For instance, can you tell me, offhand, from the list what are all the structures involved in describing an Abelian variety?
Jul
1
asked Where can I find an ontology of algebraic structures?
Nov
18
comment I almost quit self-studying mathematics, but should I continue?
Another approach is to do a taylor expansion of sqrt(1+x) around exp(i.f), square and integrate over f from 0 to 2Pi.
Nov
18
comment I almost quit self-studying mathematics, but should I continue?
Ok, I see it, but it hides a lot under the rug!
Nov
18
comment I almost quit self-studying mathematics, but should I continue?
Identifying the first series with the hypergeometric function, one easily gets $4/\Gamma(1/2)^2$. This feels like cheating of course. Can you give a hint on a more elementary approach? The term in the series can be written as $\left((2n-1)^{-1}4^{-n}{2n \choose n}\right)^2$ but I don't quite see how Vandermonde's identity plays in.
Nov
8
revised Looking for a limit
added 368 characters in body
Nov
8
comment Looking for a limit
The answer is valid in a sense for the continuous version as well, it's just that the tail is wavy and the phase varies with K, so a local derivative isn't meaningful. But for practical purposes, if you squint, the answer's the same.
Nov
8
comment Looking for a limit
The continuous version converges though, multiply $x$ by $\lambda = \left(\frac{1+a}{1-a}\right)^{\epsilon}$, you can then interpret that as shifting the integrand by $\epsilon$ and multiplying by $\lambda$. Since all of the mass is going to be in a very small region where the std is close to $x$, the continuous binomial coefficients are locally exponential and you can undo the shift by multiplying by $\left(\frac{\log (1-a)}{\log \frac{1-a}{a+1}}\right)^{\epsilon}$. This gives you the $\alpha$ in the answer.
Nov
8
comment Looking for a limit
Ok, but it still doesn't converge :) You keep getting ripples in the tail that make the local derivative meaningless.
Nov
6
awarded  Commentator
Nov
6
comment Looking for a limit
I think you really do mean $1+a(1+a)$. For instance, you say: "Thus in place of $a(1)$ we have $\frac{1}{2} a(1)( 1\pm a(2))$". You also refer to it as "uncertainty about the error rate $a(1)$". Now if you insist that what you care about is the binomial, then the answer is as above: no convergence in the discrete case, convergence in the continuous case with an analytical answer.
Nov
6
comment Looking for a limit
The last formula of page 98 is incorrect. Just take $N=2$... $(1+a(1)(1+a(2))) \neq (1+a(1))(1+a(2))$. Or simply consider that if your uncertainty is $5\%$, the largest error you can get is $.05 \times (1 + .05 \ldots )) \sim 5.263\% \ldots$
Nov
5
comment Looking for a limit
$1+a(1+a) \neq (1+a)(1+a)$, am I missing something?
Nov
5
comment Looking for a limit
But then, the variances are going to be contained in the interval $[1-\frac{a}{1-a},1+\frac{a}{1-a}]$ and there won't be any fat tails.