8,771 reputation
22040
bio website gottwurfelt.wordpress.com
location San Francisco, CA
age 30
visits member for 4 years, 2 months
seen 2 days ago

Quantitative analyst and math blogger.


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
Jul
17
comment If $n = m^3 - m$ for some integer $m$, then $n$ is a multiple of $6$
Bill, that is more clever than the solution I had in mind - I hadn't thought to exploit what was done in the original question! I was thinking of factoring as $m(m-1)(m+1)(m^2+1)$ and then arguing that at least one factor is divisible by each of 2, 3, and 5.
Jul
17
comment If $n = m^3 - m$ for some integer $m$, then $n$ is a multiple of $6$
You might also want to show that if $n = m^5-m$ for some integer $m$, then $n$ is a multiple of 30. (This is a bit trickier but basically the same idea.)
Jul
16
comment Mathematics behind a programming puzzle
The $c_i$ are not necessarily all the same, so you can't borrow known results about the Irwin-Hall distribution.
Jul
10
comment Is there a sequence in $(0,1)$ such that the product of all its terms is $\frac{1}{2}$?
To see that the terms are in the desired range, it helps to write a formula for $x_n$ in terms of $n$.