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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.


Mar
14
comment How likely is it not to be anyone's best friend?
I wonder what, say, Facebook's data on this would look like, where "best friend" would be defined as "person most interacted with on Facebook". Of course this has nothing to do with your model.
Feb
4
comment Expected value of first head in coin toss.
Since $X$ is a discrete random variable, you should take the sum $\sum_x x f_X(x)$, not the integral.
Jan
31
comment Inverse birthday estimation
Possible duplicate of math.stackexchange.com/questions/114544/… ?
Jan
31
comment Inverse birthday estimation
Yes, it's natural log. I don't know a name for this problem, although that doesn't mean there isn't one.
Dec
31
comment What's the name of this quantity?
We have $M_n \ge \lfloor n^2/2 \rfloor$, since $dist(\sigma_n) = \lfloor n^2/2 \rfloor$ when $\sigma_n$ is the ``reverse'' permutation $n(n-1)(n-2) \ldots 1$. This is the sequence oeis.org/A007590. But I can't prove that this is an equality.
Dec
12
comment Proof of inequality with ratio of odds to evens.
This actually may have to do with calculus, depending on what you've learned - take logs of all three members of the inequality and you've converted the problem into showing that a certain sum is between $-\log 2 - \log n$ and $-{1 \over 2} \log 2 - \log n$. If my intuition is right, there are two integrals which are lower and upper bounds for that sum and which have those values. (Comment instead of answer because I haven't worked out the details so I don't know if this works.)
Oct
28
comment Maximum bin load for $\alpha n$ balls into $n$ bins
It would help if you gave a reference to the paper.
Oct
4
comment Baseball, batting average, and probability
Sabermetrics folks have already looked into this: see for example here, here, here.
Aug
22
comment Elementary statistics problem
If you're being asked to solve this problem, you have probably seen a few inequalities named after Russians.
Aug
19
comment Longest known sequence of identical consecutive Collatz sequence lengths?
That's because the "Collatz path" of nearby numbers often coalesces. To take a simple example, there are sequences starting 36-18-9-28 and 37-112-56-28. Both have one upward step and two downward steps, but in different orders. Lopsy's heuristic doesn't know about this.
Aug
19
comment Longest known sequence of identical consecutive Collatz sequence lengths?
See oeis.org/A008908. There's a sequence of length 17 starting at 7083. After 36 steps, the sequence of iterates of 7083 through 7099 all coalesce at 76; they all reach 1 at step 58.
Aug
18
comment Longest known sequence of identical consecutive Collatz sequence lengths?
I'd note that this depends on how you define "Collatz sequence" - does an odd n get mapped to 3n+1, or to (3n+1)/2? (You've chosen the first one.)
Aug
2
comment Splitting Stacks Nim
@MJD: I'm curious. I'm curious enough that I may just write the code myself.
Aug
2
comment Splitting Stacks Nim
MJD: is the nim-value actually determined by the number of pennies and the number of piles, for the sample that you checked?
Jul
16
comment Determine which mean is smaller over two non-normal distributions
You want the Mann-Whitney U test: en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U
Jul
16
comment Packing rectangles in a grid
There are good heuristics for packing a car with suitcases. (I don't know what these are, but my father does. I've seen him do it.)
Jun
24
comment Probability that random subspaces intersect
And if $a + b < d$ (for example, two lines in 3-space) this will be zero. The nontrivial case is $a+b = d$.
Jun
11
comment Unexpected approximations which have led to important mathematical discoveries
Not exactly what you're asking, but Noam Elkies has a short explanation of why $\pi^2 \approx 10$: math.harvard.edu/~elkies/Misc/pi10.pdf
Jun
3
comment Using math for interior decorating with lamps
The response to a light stimulus isn't directly proportional to the stimulus. Rather it's proportional to the logarithm of the stimulus - this is the "Weber-Fechner law" (en.wikipedia.org/wiki/Weber%E2%80%93Fechner_law). So maybe work with $\log (a^{-2} + b^{-2} + c^{-2})$. This is both psychophysically more realistic and won't diverge as badly around the lights themselves. In particular you can calculate the average light level in the room, which you couldn't do without the logs.
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.