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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
Jun
21
accepted What's the minimum of $\int_0^1 f(x)^2 \: dx$, subject to $\int_0^1 f(x) \: dx = 0, \int_0^1 x f(x) \: dx = 1$?
Jun
20
comment Is the Iterated Continued fraction from Convergent​s for Pi/2 exactly 3/2?
So I don't know much about this, but is it possible that this process always converges to $3/2$, or at least does so for starting points in a fairly wide range? That seems more likely than that this is some special property of $\pi/2$.
Jun
20
comment What's the minimum of $\int_0^1 f(x)^2 \: dx$, subject to $\int_0^1 f(x) \: dx = 0, \int_0^1 x f(x) \: dx = 1$?
Well, there is the same mysterious constant of 12. I may give it a shot.
Jun
20
asked What's the minimum of $\int_0^1 f(x)^2 \: dx$, subject to $\int_0^1 f(x) \: dx = 0, \int_0^1 x f(x) \: dx = 1$?
Jun
20
comment Three consecutive sums of two squares
The sequence of numbers n such that n, n+1, n+2 are all sums of two squares is given at oeis.org/A082982 . (As you'd expect, they're all multiples of 8.) This sequence doesn't look to me like there's a nice formula. Of course this doesn't prove there isn't one.
Jun
20
comment What resources are there for learning Russian math terminology?
While browsing in the library a couple weeks ago I came across "Russian for the Mathematician" by Sydney H. Gould. This might be what you're looking for. There appear to be very cheap used copies available if your library doesn't have it.
Jun
17
awarded  Nice Answer
May
31
comment Simple way to measure or calculate the volume of clothing?
There's a lot of air in clothing, as anybody who's squashed down a suitcase to get more into it knows. See also those vacuum-storage bags that are advertised on late night television.
May
31
comment On doubly graceful permutations
Vote for Yuval's answer! He actually solves the problem instead of just idly speculating.