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May
14
answered A simple problem about partition function and Young diagram
May
14
comment Intuitive understanding of why the sum of nth roots of unity is $0$
I came here to give this explanation but I see I was beaten to it. Good job.
May
13
awarded  Nice Answer
May
9
comment If you randomly choose a subset of the real line, what is the probability that it will be measurable?
The answer has to be zero. If not, I don't believe in choice.
May
7
answered Variance for summing over distinct random integers
May
6
comment Is there an unambiguous way to define the average (and higher moments) for a probability density on a circle?
@Didier: basically all I know about directional statistics is that they have a Wikipedia article.
May
6
comment Is there an unambiguous way to define the average (and higher moments) for a probability density on a circle?
There exists something called "directional statistics": en.wikipedia.org/wiki/Directional_statistics .
May
6
comment Does another chain of three squares in this manner exist?
See oeis.org/A031150 and oeis.org/A023110, although there doesn't seem to be a huge amount to work with there.
May
5
comment Optimizing the expectancy
That is, what Ross said.
May
5
comment Optimizing the expectancy
Obvious generalization time: for $k$ stations, I'm guessing that the optimal locations are at $1/(2k), 3/(2k), \ldots, (2k-1)/(2k)$, by this same proof but with more variables.
May
4
answered A combinatorial card problem
May
3
comment Is the $\sum\sin(n)/n$ convergent or divergent?
How does one prove that formula for the sum? I'm guessing that writing $sin(n) = (e^{in} - e^{-in})/(2i)$ and then following your nose gives the result, but I haven't tried it.
May
3
comment Need a result of Euler that is simple enough for a child to understand
There's a nice bijection between the two, as well, which usually goes under the name of "Glaisher's bijection".
May
3
revised $N^L$ vs. ${N+L\choose N}$
added 10 characters in body
May
2
answered $N^L$ vs. ${N+L\choose N}$
May
2
comment How to find the number of continued fraction from a periodic representation?
If you put a number into Wolfram Alpha it'll give you back its continued fraction representation. This isn't the direction you're trying to go, but it'll help you check your work.
May
2
comment Expected value of max/min of random variables
So in the limit where $n$ is large (lots of urns) and $k = \alpha n$, the number of balls in urn $i$ will be approximately Poisson with mean $\alpha$. Furthermore if $n$ is large then the counts in the different boxes will be approximately independent. So you can probably get an approximate answer starting from this using order statistics methods, as Henry suggested.
May
2
comment Modulo arithmetic with big numbers?
I'd just like to point out that repeated squaring is not necessarily the fastest way to do this. The more general "addition-chain exponentiation" (en.wikipedia.org/wiki/Addition-chain_exponentiation) can sometimes require less multiplications. However, it's a lot harder to figure out which multiplications to do.
Apr
28
revised Computing the population given a set of replication rates
added tags
Apr
28
answered Calculus one problem about substitution and area