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Jul
22
awarded  Yearling
Jul
21
comment What is a cubical sphere?
So a combinatorial cube is something that has the same inclusions among its faces as the usual $n$-cube?
Jul
21
comment What is a cubical sphere?
How do you define "combinatorial cubes"?
Jul
18
comment Bullseye distribution (Rayleigh distr)
I agree with this guess.
Jul
14
answered The probability that 25 people do not have the same birthday
Jul
7
comment The “beach problem”: does anyone know it? or know how to solve it?
I don't read German. Is this basically just a brute-force search or is there something more going on?
Jul
6
comment How accurately can huge factorials be calculated?
The last term in your sum should be $\log \sqrt{n}$ or ${1 \over 2} \log n$.
Jul
5
comment What technique would be suitable to solve this: $\int \sin ^{5}\left( x^{2}\right) \left( x\cos \left(x^{2}\right)\right)\mathrm{d}x$
$x^2$ is "ugly". So we call it $u$, the first letter of "ugly".
Jul
5
comment Recursion equations: $T(n)=T(\frac{n}{4})+T(\frac{3}{4}n)+1$
The next natural question is to ask for $\lim_{n \to \infty} T(n)/n$. Since $n/4$ and $3n/4$ are not necessarily integers this depends on how you round; the correct way to do this presumably comes from the algorithm that gives rise to this recurrence. But it appears that for any combination of rounding up, rounding down, and rounding to the nearest integer that limit doesn't exist; rather $T(n)/n$ oscillates between two constants $a$ and $b$.
Jul
5
comment Five Fridays and Sundays on October
It actually showed up in my e-mail. (From someone who seems to think I'm someone they know and has the wrong e-mail address for me. Everyone I know knows better than to send me things like this.)
Jul
4
comment Probability metric spaces for which $r \leq R$ implies $\frac{Pr(B(x,r))}{Pr(B(x,R))} \geq \frac{r}{R}$
The first thing that comes to mind is that if you're working in the $d$-dimensional unit cube, then (except near the edges) $Pr(B(x,r))/Pr(B(x,R)) = (r/R)^d$. So in some sense you want spaces which are of dimension one or less.
Jul
2
comment Shortest sequence containing all permutations
9 is correct for $s^\prime(3)$ where $s^\prime$ is the substring version of the problem. It's obvious any string of this type has to be at least of length 8, so that it has enough substrings. But if it's of length 8 then every substring has to be different, so you start constructing the string 12312ohcrap. 123121321, of length 9, works.
Jul
1
comment sum of independent random variables
In general you want to find the density of $Z$ and invert it. How to do this efficiently is going to depend very strongly on the specifics of the problem; what specifically are you interested in?
Jun
30
comment Equality of outcomes in two Poisson events
I thought of this but got tripped up on what the bounds on the integral should be; that's why I made the second transformation, from Poisson to binomial.
Jun
30
comment Equality of outcomes in two Poisson events
If it helps, assume throughout that $\lambda$ is an integer. Since we're worrying about the limit as $\lambda \to \infty$ it seems quite likely that we can just find the answer for integer $\lambda$ and wave our hands about the solution being smooth. That being said, I don't intend this to be a fully rigorous proof.
Jun
30
answered Equality of outcomes in two Poisson events
Jun
29
comment Enlightening misunderstandings of test questions
Joel, I knew a guy in high school who, when asked on a physics test to "name the force acting on this object", named it "Bob".
Jun
23
comment Formula for occurrence of leap years in the Jewish calendar
I haven't thought about it, but I would imagine that for the sets that are likely to occur in calendar applications -- that is, where the leap years are roughly evenly spaced -- you're more likely to get "lucky" than you would than for sets chosen uniformly at random.
Jun
21
awarded  Nice Question
Jun
21
awarded  Scholar