10,451 reputation
22251
bio website gottwurfelt.wordpress.com
location Atlanta, GA
age 31
visits member for 4 years, 6 months
seen 8 hours ago

Data scientist and math blogger.


Apr
5
comment Sum of series $\sum_{k=1}^\infty{-\frac{1}{2^k-1}}$
I'm not really a number theorist. But computing $\tau(n)$ in general would be at least as hard as primality testing, since $n$ is prime if and only if $\tau(n) = 2$.
Apr
5
comment How do we arrive at the conclusion that P(Head) =0.5 for a fair coin?
Why am I not surprised that Diaconis has worked on this?
Apr
5
comment Intermediate Text in Combinatorics?
Bona also has a book at a higher level than "A Walk Through Combinatorics", entitled "Introduction to Enumerative Combinatorics". I don't know this book but if it's in your library it's probably worth looking at.
Apr
5
comment Usefulness of Variance
You're right about the dice.
Apr
5
comment Usefulness of Variance
I think it's interesting that we gave essentially the same answer.
Apr
5
answered Usefulness of Variance
Apr
5
comment How do we arrive at the conclusion that P(Head) =0.5 for a fair coin?
Amit: whether a coin comes up heads depends only on the position and orientation that it has when it leaves your hand and the velocity and angular momentum that you give it. (I may not have the list exactly right, but the point is it's some short list of classical physical quantities.) If we knew these quantities exactly we could tell in advance whether the coin will land heads or tails.
Apr
5
comment How do we arrive at the conclusion that P(Head) =0.5 for a fair coin?
Eric: the Gelman-Nolan article mentions an experiment by Kerrich where a wooden disc was coated on one side with lead; the non-coated side faced down 679 times out of 1000.
Apr
5
comment How do we arrive at the conclusion that P(Head) =0.5 for a fair coin?
Eric: I didn't completely specify the model. In some proportion of coin tosses the coin will be close to vertical when it hits the ground. Then the weight distribution might become relevant. Strictly speaking, my argument only applies to the position of the coin while it's in the air.
Apr
5
comment How do we arrive at the conclusion that P(Head) =0.5 for a fair coin?
Arturo, isn't "how close" supposed to be proportional to $1/\sqrt{n}$?
Apr
5
answered How do we arrive at the conclusion that P(Head) =0.5 for a fair coin?
Apr
5
answered Sum of series $\sum_{k=1}^\infty{-\frac{1}{2^k-1}}$
Mar
31
comment Representing Ternary as Binary: Probability that the first $n$ bits are all zero
My instinct is that your random ternary numbers, when represented in binary, will look just like random numbers. In particular their probability of ending in $n$ zeros should be about $2^{-n}$.
Mar
28
comment How to show that $\sum\limits_{k=1}^{n-1}\frac{k!k^{n-k}}{n!}$ is asymptotically $\sqrt{\frac{\pi n}{2}}$?
I think you can find this somewhere in Flajolet and Sedgewick, Analytic Combinatorics. (At least I'm sure they quote the result; I'm not sure if they derive it, but if they don't derive it they give a source that does.) This book is available online. But I don't have time to track down the reference more precisely, so this comment may be of little help as it's an 800-page book.
Mar
28
answered Sum the infinite series $ \sum_{n=0}^\infty (2n^7 + n^6 + n^5 + 2n^2)/n! $
Mar
28
comment Finding the first 5 terms of a Maclaurin Series using division?
For general $f(x)/g(x)$, this probably isn't much savings. But since we happen to know the series for $1/g(x)$ here, yeah, I think it helps.
Mar
28
answered How does one get the formula for this bijection from $\mathbb{N}\times\mathbb{N}$ onto $\mathbb{N}$?
Mar
25
answered Is there a geometric interpretation of the exponential function of real numbers?
Mar
25
comment What are the 2125922464947725402112000 symmetries of a Rubik's Cube?
Okay -- so the $2^{12}$ is actually $4^6$ (orientations of the central squares) and the remaining factor of 12 is the usual one for the Rubik's cube.
Mar
25
comment What are the 2125922464947725402112000 symmetries of a Rubik's Cube?
For what it's worth, this is 49152, or $2^14 \times 3$, times the number that's usually given. I'm not sure how to make sense of this but it may be helpful.