8,356 reputation
21537
bio website gottwurfelt.wordpress.com
location San Francisco, CA
age 30
visits member for 3 years, 9 months
seen Apr 8 at 18:07

Quantitative analyst and math blogger.


Dec
14
comment How many citations to read before convergence?
When you start seeing the same papers over and over again, that's when you're done.
Dec
6
comment How to shuffle a deck of cards?
So now we just need $n^n/n!$ to not be an integer. It's not.
Dec
6
answered How to shuffle a deck of cards?
Nov
28
comment “How long 'til we get there?” Road trip puzzle
US road signs do have text on them, so if there were a town called "Speed Limit" this could theoretically happen.
Nov
27
comment Dividing a range into major and minor divisions
You're welcome! Glad to hear it works - I was pretty much just thinking out loud and didn't do any testing, so I could have said something stupid.
Nov
27
comment “How long 'til we get there?” Road trip puzzle
You might find the ending of Billy Jonas's song "Wichita" to be of interest. Lyrics at billyjonas.com/index.php?page=songs&display=57 .
Nov
27
answered Dividing a range into major and minor divisions
Nov
25
comment Entropy of a binomial distribution
A comment: the entropy of the normal distribution with variance $\sigma^2$ is ${1 \over 2} \log (2\pi e \sigma^2)$, which can be computed by a fairly straightforward integration. Perhaps using Stirling's approximation you can reduce the computation of the entropy of the binomial to this same integral plus some error terms. (I haven't actually tried to do this.)
Sep
21
awarded  Custodian
Sep
4
answered Proving an equality involving compositions of an integer
Sep
4
comment “Rules of thumb” to decide which convergence test is most appropriate
One good rule of thumb is to apply the "easiest" tests first -- so if it looks easy to take the ratio of consecutive terms, take ratios. (This includes if $a_n$ contains factorials, since most of the factors will cancel.) If $a_n$ contains $n$th powers, try the root test first.
Aug
31
answered A couple of asymptotics exercises
Aug
31
comment A couple of asymptotics exercises
You only need it for real $z$. If you're willing to assume that $\Gamma(z)$ is an increasing function (which follows from the definition of $\Gamma$ as an integral) then it will suffice to show that $z! \ge (z+1)^{(z+1)/2}$ for large enough integers $z$. This lower bound is bigger than the previous one by a factor of about $\sqrt{ez}$, which is pretty much negligible. (At some point, if you're going to worry about this sort of thing, you should just throw in the towel and use Stirling.)
Aug
31
answered A couple of asymptotics exercises
Aug
25
comment Limit of sum of indicator function
Can you interpret this limit as the probability of some event? (Hint: yes.)
Aug
24
comment Accidents of small $n$
It's fun to point out to people that the sequence contains 256; that provides extra "evidence" that it consists of powers of two!
Aug
24
comment Theorems with an extraordinary exception or a small number of sporadic exceptions
I liked this fact a lot two years ago. I'm 28.
Aug
24
comment Theorems with an extraordinary exception or a small number of sporadic exceptions
I'm not sure the third one really counts. I could say "all primes other than three are not multiples of three." It's just that we don't have a special name for numbers that aren't multiples of 3.
Aug
22
comment $x,y,z$ independent and uniform random on $[0,1]$, $P(x \geq yz)$?
The beta(1,2) distribution is also the distribution of the minimum of two independent uniform[0,1] random variables $X$ and $Y$. (This is a standard result in the theory of order statistics.) In order to have $min(X,Y) \le 1/2$ we must have $X \le 1/2$ or $Y \le 1/2$, which obviously has probability 3/4.
Aug
12
answered Game theory - self study