Michael Lugo
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 Oct 5 answered calculating n choose k mod one million Oct 5 revised Baby Shower Problem. Too hard for 1st grader but got parents thinking (1,0) and (0,1) aren't solutions in practice Oct 5 comment Baby Shower Problem. Too hard for 1st grader but got parents thinking That's a good point. I'll edit to reflect this. Oct 4 answered Baby Shower Problem. Too hard for 1st grader but got parents thinking Oct 4 answered Bounds on expected value and distribution of a product of beta random variables Oct 4 comment Asymptotics of LCM Consider $f_1(n) = 2^n$ and $f_2(n) = 2^n-1$, then. Then the LCM of the second sequence grows much faster than that of the first. Oct 1 comment What is the asymptotic bound for this recursively defined sequence? I'm not sure if you can just say "rolling back" like that here. From computing $g(n)$ out to $2^{10}$ (which I admit isn't that far) it seems like $f(2^n) \sim c 2^{n+2}$ as $n \to \infty$ but, say, $f(3 \times 2^n)$ isn't necessarily approaching $c (3 \times 2^{n+2})$. Is there some theorem encapsulated in the phrase "rolling back" that I'm unaware of? Sep 30 answered Manipulating harmonic series Sep 30 comment Manipulating harmonic series I cleared up your notation. In particular it's not true that $\sum_{k=1}^n {1 \over k} = \ln n$ exactly; it's only approximately true. Sep 30 revised Manipulating harmonic series cleaned up TeX Sep 28 comment Dependence of certain random variables Thanks. This is what happens when I write quickly. Sep 28 comment Why is $f(x) = x\phi(x)$ one-to-one? $n\phi(n) = \phi(n^2)$, which might help. Sep 28 comment Rolling dice such that they add up to 13 — is there a more elegant way to solve this type of problem? If you want to learn more about generating functions, you should take a look at Herb Wilf's book "generatingfunctionology", which can be found free online. (This is legal; Wilf has posted the book on his web page.) This book is probably best read after you know some combinatorics and some probability. Sep 27 answered How would I solve $\frac{(n - 10)(n - 9)(n - 8)\times\ldots\times(n - 2)(n - 1)n}{11!} = 12376$ for some $n$ without brute forcing it? Sep 27 answered Dependence of certain random variables Sep 27 answered Rolling dice such that they add up to 13 — is there a more elegant way to solve this type of problem? Sep 23 comment Why does volume go to zero? Came into this thread to give this proof, but I see someone beat me to it. Sep 20 comment Can you answer my son's fourth-grade homework question: Which numbers are prime, have digits adding to ten and have a three in the tens place? I agree. But my gut feeling (which I admit may be wrong!) is that that non-independence only shows up in the constant factors that I've suppressed. Sep 20 awarded Nice Answer Sep 20 answered Can you answer my son's fourth-grade homework question: Which numbers are prime, have digits adding to ten and have a three in the tens place?