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May
3
revised $N^L$ vs. ${N+L\choose N}$
added 10 characters in body
May
2
answered $N^L$ vs. ${N+L\choose N}$
May
2
comment How to find the number of continued fraction from a periodic representation?
If you put a number into Wolfram Alpha it'll give you back its continued fraction representation. This isn't the direction you're trying to go, but it'll help you check your work.
May
2
comment Expected value of max/min of random variables
So in the limit where $n$ is large (lots of urns) and $k = \alpha n$, the number of balls in urn $i$ will be approximately Poisson with mean $\alpha$. Furthermore if $n$ is large then the counts in the different boxes will be approximately independent. So you can probably get an approximate answer starting from this using order statistics methods, as Henry suggested.
May
2
comment Modulo arithmetic with big numbers?
I'd just like to point out that repeated squaring is not necessarily the fastest way to do this. The more general "addition-chain exponentiation" (en.wikipedia.org/wiki/Addition-chain_exponentiation) can sometimes require less multiplications. However, it's a lot harder to figure out which multiplications to do.
Apr
28
revised Computing the population given a set of replication rates
added tags
Apr
28
answered Calculus one problem about substitution and area
Apr
28
comment Number of ways of dividing $n-m$ into parts of at most size $m$
missou: This question is a bit cryptic. Can you explicitly list the ways of dividing $n-m$ into (something) of at most size $m$ for some small numbers $n$ and $m$, so that we have a better idea of what you mean?
Apr
28
awarded  Good Answer
Apr
23
comment Find a way from 2011 to 2 in four steps using a special movement
You're right. I obviously didn't bother to check that.
Apr
22
comment Find a way from 2011 to 2 in four steps using a special movement
Are we supposed to assume that $p$ and $q$ are relatively prime?
Apr
22
awarded  Taxonomist
Apr
21
revised Uniform Distributions - Probability
added 3 characters in body
Apr
21
comment Last two digits of $2^{1000}$ via Chinese Remainder Theorem?
If you want a similar problem that does use the CRT: what are the last two digits of $3^{1000}$?
Apr
20
comment Density and expectation of the range of a sample of uniform random variables
The derivation of the joint density of order statistics is as follows: we want the probability that $U_{(i)}$ is in some small interval $[u, u + du]$ and $U_{(j)}$ is in some small interval $[v, v + dv]$. This amounts to finding the probability that $i-1$ of $U_1, \ldots, U_n$ is less than $u$, one is in $[u, u + du]$, $j-i-1$ are between $u+du$ and $v$, one is in $[v, v + dv]$, and the remaining $n-j$ are greater than $v$. The five clauses of the previous sentence give the five factors; the embedded combinatorial problem gives the premultiplying factor.
Apr
20
comment Prove $\sin(\pi/2)=1$ using Taylor series
What do you mean by the usual definition of $\pi$? I'm thinking you mean the ratio of circumference to diameter, which in this context can be written as an integral?
Apr
19
awarded  Quorum
Apr
19
comment Finding distribution functions of exponential random variables
This is a standard fact about the gamma distribution; it's actually derived by integration.
Apr
19
comment Density Question - Statistics
This happens to involve the chi-square distribution, but the chi-square distribution is just a gamma distribution.
Apr
18
answered Finding distribution functions of exponential random variables