PeterR
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 Jan16 comment Fun but serious mathematics books to gift advanced undergraduates. +1 for "Proofs and Confirmations" by David Bressoud. It is ridiculously good. Nov29 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. Nov29 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))? Oct22 awarded Yearling Oct19 answered How to prove $\nabla\cdot \vec{B}=0 \Rightarrow \exists \vec{A}:\vec{B}=\nabla \times \vec{A}$ Oct5 awarded Critic Sep6 answered $\sum_{k=1}^{\infty} \ln{\left(1 + \frac{1}{4 k^2}\right)}$ Computing this sum Jul17 comment What does the variance/SD of a set signify? See the chebyshev inequality. May17 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. May6 asked Describe growth of $\epsilon n$ Mar22 awarded Commentator Mar9 accepted Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$ Mar9 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! Mar9 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 $\exp(n p^k) \approx 1$? Mar9 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 $\frac{\log n}{\log\frac{1}{p}}$? Mar8 asked Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$ Feb23 answered Examples to show intersection of two uncountable sets can be countably infinite Feb7 answered Confused about permutation cycles - Question on joint cycles of odd length Feb1 answered Popular math books with depth Oct22 awarded Yearling