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Jan
16
comment Fun but serious mathematics books to gift advanced undergraduates.
+1 for "Proofs and Confirmations" by David Bressoud. It is ridiculously good.
Nov
29
comment Example of two dependent random variables that satisfy $E[f(X)f(Y)]=Ef(X)Ef(Y)$ for every $f$
@NateEldredge: that is what I figured. So if you do the arithmetic, it does not work out. f(1)P(X=1)+f(2)P(X=2)+f(3)P(X=3)=(5x+9y+12z)/30, not (3x+3y+4z)/10....unless I'm seriously caffeine deficient right now.
Nov
29
comment Example of two dependent random variables that satisfy $E[f(X)f(Y)]=Ef(X)Ef(Y)$ for every $f$
Can you pls explain how you got E(f(X))?
Oct
22
awarded  Yearling
Oct
19
answered How to prove $\nabla\cdot \vec{B}=0 \Rightarrow \exists \vec{A}:\vec{B}=\nabla \times \vec{A}$
Oct
5
awarded  Critic
Sep
6
answered $ \sum_{k=1}^{\infty} \ln{\left(1 + \frac{1}{4 k^2}\right)}$ Computing this sum
Jul
17
comment What does the variance/SD of a set signify?
See the chebyshev inequality.
May
17
comment What's the sum of $\sum_{k=1}^{\infty} e^{-k(x-k)^{2}}$?
Look up the Euler Maclaurin formula....Mathematica can do the integral, and it involves the erf function.
May
6
asked Describe growth of $\epsilon n$
Mar
22
awarded  Commentator
Mar
9
accepted Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
Mar
9
comment Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
@RobertIsrael: Phew - now I can drink the coffee slowly, rather than chugging it. That helps a huge amount, much appreciated!
Mar
9
comment Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
@RobertIsrael: Thanks much. There are still (at least) two things I'm not getting. You say $\exp(n \log(1-p^k)) \approx \exp(n p^k)$, shouldn't it be $\exp(n \log(1-p^k)) \approx \exp(-n p^k)$ (negative sign)? And why are we solving $npk \approx 1$ Since this is the size of the term $f(k,n)$, wouldn't we want it to be $\exp(n p^k) \approx 1$?
Mar
9
comment Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
@RobertIsrael: Thanks for the helpful comments. I too had thought about splitting the summation into two parts, one with terms close to zero, the other with terms close to one, but didn't see how to choose the splitting point appropriately. How did you decide on $\frac{\log n}{\log\frac{1}{p}}$?
Mar
8
asked Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
Feb
23
answered Examples to show intersection of two uncountable sets can be countably infinite
Feb
7
answered Confused about permutation cycles - Question on joint cycles of odd length
Feb
1
answered Popular math books with depth
Oct
22
awarded  Yearling