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bio website gottwurfelt.wordpress.com
location San Francisco, CA
age 30
visits member for 4 years, 2 months
seen 21 hours ago

Quantitative analyst and math blogger.


2d
comment Proving $\frac{1}{\sin^{2}\frac{\pi}{14}} + \frac{1}{\sin^{2}\frac{3\pi}{14}} + \frac{1}{\sin^{2}\frac{5\pi}{14}} = 24$
If I'm not mistaken, this generalizes to give $\sum_{k=1}^n \csc^2 (k\pi/(2n+1)) = 2n(n+1)$, with $n = 3$ being the original question.
Sep
15
comment Random walk on a finite square grid: probability of given position after 15 or 3600 moves
For a related blog post see John Cook's post.
Aug
15
comment Is there a name for the function $\max(x, 0)$?
It should be noted that the negative part is, in fact, a positive number. For example the negative part of -3 is 3.
Aug
5
comment Asymptotic behavior of $\sum\limits_{k=1}^n \frac{2^k}{k}$
Call your sum $S_n$. Let $T_n = S_n/2^n$; then it's not hard to show that $T_1 = 1$, $T_n = T_{n-1}/2 + 1/n$. You want to show $T_n \sim 2/(n+1)$. Not sure this helps.
Jul
16
comment Probability of Random Variable Minus Random Variable
There are quantitative bounds on the approximation such as the Berry-Esseen inequality, but those are almost surely beyond the scope of the course the poster is taking.
May
15
comment Probability of getting better than a certain score
Andre, you can always just run a more involved simulation (more trials, or compute some other intermediate results) if you want a coffee break.
May
9
comment How prove this frog can finite steps jump the point $(\frac{1}{5},\frac{1}{17})$
If I understand the problem correctly, a jump like (1/17, 4/17) isn't allowed since it's not of length 1. But you could use (8/17, 15/17) in this context.
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.