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21738
bio website gottwurfelt.wordpress.com
location San Francisco, CA
age 30
visits member for 4 years
seen 14 hours ago

Quantitative analyst and math blogger.


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
Aug
10
answered Product of all primes less then x
Aug
9
answered Estimate Stirling numbers from normal distribution?
Aug
8
comment Greatest common denominator of measurements
I don't know, but this is actually a question I wondered about when I first learned about the Millikan experiment. It's possible that you can just get enough data not to worry about it. If you're really curious you might go and find the original paper and see whether Millikan worried about it.
Aug
4
comment What are the chances of three consecutive hands of all vowels in Scrabble?
Good point. So we should have ${38 \choose 11}/{92 \choose 11} \approx 2.2 \times 10^{-5}$.
Aug
4
answered What are the chances of three consecutive hands of all vowels in Scrabble?
Aug
3
comment How do I calculate the probability distribution of the percentage of a binary random variable?
This is, I think, a lucky guess, but it's actually the right lucky guess. However I'd point out that there's no reason you should necessarily start with B(1,1). If you want to learn more you should read up a bit on Bayesian statistics, which is what you're trying to do.
Aug
1
comment Is there a Hamiltonian path for the graph of English counties?
Is there a Hamiltonian path for the 48 contiguous US states? (It would have to start or end in Maine.)
Jul
27
awarded  Nice Answer
Jul
25
answered A (probably trivial) Induction Problem: $\sum_2^nk^{-2}\lt1$
Jul
21
awarded  Yearling