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Jan
20
comment Mathematics understood through poems?
Updating the broken links: maa.org/press/periodicals/convergence/… maa.org/press/periodicals/convergence/… etc.
Dec
15
comment Expected Number of Coin Tosses to Get Five Consecutive Heads
I found an answer using martingales here: quora.com/… but I'm curious if there is a generating functions way (also about the distribution, say variance or number of trials until 90% probability of seeing what we want).
Dec
15
comment Expected Number of Coin Tosses to Get Five Consecutive Heads
Do you know how to find the distribution (or expectation and variance) for the number of tosses until either 5 consecutive heads or 5 consecutive tails? (Or 5 consecutive equal results from rolling dice.) Is there a question on math.se about this?
Nov
13
comment $e^{e^{e^{79}}}$ and ultrafinitism
@FanZheng Bases don't have to be integers; see Wikipedia articles on Non-integer representation and base-φ. For the rest, I've already explained the issue in my previous comments; I don't know which part is unclear. You might also want to look at this question which is about the "every base is base 10" joke.
Sep
11
comment Is this Batman equation for real?
I just found out that the curve was devised by J. Mathew Register (then "teaching at a few art schools throughout the greater Sacramento area", now "a full time professor over at American River College"): quora.com/Who-wrote-the-Batman-equation/answer/…
Jul
27
comment Recurrence relation with generating function problem
I agree; that's part of why it's less simple in this case.
Jul
22
comment Fast way to get a position of combination (without repetitions)
@van E.g. on SO: stackoverflow.com/questions/3143142/… stackoverflow.com/questions/5307222/… (and many others). On this site: math.stackexchange.com/questions/349924/… (and many others). On Wikipedia: en.wikipedia.org/wiki/Combinatorial_number_system en.wikipedia.org/wiki/Factorial_number_system Terms to search for are "(ranking|indexing) combinations", also "combinadics", and names of those WP articles.
Jul
22
comment Simple string permutations question
The answer is correct, but if you're writing it up for homework / an exam etc., you should add that $\binom{5}{2}$ is the number of ways to allocate the positions of the vowels in the sequence.
Jul
22
comment Playing roulette
@nknj: Thanks, fixed.
Jul
21
comment Fast way to get a position of combination (without repetitions)
This question has been asked before multiple times on both this website and StackOverflow; one of the existing answers may suit you. (That's assuming that your $\left(\!\!\binom{n}{k}\!\!\right)$ is just an odd way of writing $\binom{n}{k}$ because I don't know what else it could mean.)
Jul
15
comment What is the most efficient numerical base system?
@alex.jordan: Indeed, looks like I made exactly that mistake, thanks for pointing it out.
Jun
28
comment search on a split data structure
BTW, $b(n)$ is $n$ for the unsorted list as you always need to look at all elements before concluding it isn't there.
Jun
28
comment Special representation of a number
The remarkable resemblance of the two plots is interesting though, and I'm curious what the general shape (of the "upper" and "lower" curves) are.
Jun
28
comment search on a split data structure
It still wasn't clear so I've edited the question; take a look and see if that's what you intended.
Jun
28
comment search on a split data structure
Can you edit the question to make it clearer in the formatting which parts are quotation from the test / homework / question, and which parts are your own thoughts / questions?
Jun
26
comment How many algebras are there of finite-sized $\Omega$?
I just got a notification because this answer was upvoted. Not only do I have no recollection of having posted this answer, I don't even understand it now. At all. Clearly the explanation could have been better!
Jun
26
comment Expectation value of number of drawings of increasing sequences of labelled balls from an urn.
@uomoinverde The bounty doesn't matter so much; what would be gratifying would be if you indicated that you understood the ideas better now. :-)
Jun
26
comment Expectation value of number of drawings of increasing sequences of labelled balls from an urn.
Note that the question asks for the probability that the number of drawings is greater than $k$, but you seem to be calculating $\Pr(X \ge k)$ instead of $\Pr(X > k)$ (which is what it asks for).
Jun
18
comment How to determine growth rate of coefficients of generating function
@Michael Yes, their Chapter VIII on the saddle-point method covers such generating functions.
Apr
15
comment Maximizing profit (dynamic programming)
More precisely: how many of questions up to 18 did you solve? Why attempt 19?