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Jul
14
suggested suggested edit on Expected Number of Coin Tosses to Get Five Consecutive Heads
Jul
4
comment Combinatorics: Mean and Variance of an indicator function of items arranged in a circle.
confirmed by this matlab quick test: n=25; b=10; X = zeros(10000,1); for i=1:length(X) B = sort(randsample(n,b)); % blue balls C = diff([B; B(1)+n]); % differences to right neightbor clock-wise D = circshift(C, 1); % differences to left neightbor clock-wise X(i) = sum(C>1 & D>1); end E = mean(X) % 3.8182 V = var(X) % 2.8490
Jun
28
comment Combinatorics: Mean and Variance of an indicator function of items arranged in a circle.
I think with a circle, all $X_i$ are equivalents, the same problem with balls on a straight line would be more difficult
Jun
27
comment Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
@Tunk-Fey contour integration comes with the study of holomorphic functions (functions continuous in $\Bbb C$)
Jun
25
accepted partial derivatives of Dirac functions
Jun
25
comment partial derivatives of Dirac functions
right, indeed, $\delta = \delta_0$ and $x_i$ is null
Jun
25
asked partial derivatives of Dirac functions
Jun
21
comment Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
Thanks, awesome answer, the trick is to take this quarter circle
Jun
20
comment Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
I guess you take a half-circle as contour, I can't get your first equality with $\sqrt i$, could you expand please?
Jun
14
comment How many are possibilities to build count $n$ summing $k$ other counts?
you forgot 5+0+0
Jun
14
comment How many are possibilities to build count $n$ summing $k$ other counts?
What are the scores for (5,3), (5,4), (5,5), (5,6)?
Jun
4
comment Multiplying using reciprocal, addition and subtraction
Are you sure it isn't $*/*$ (division of any pair) instead of inverse $1/*$?
Jun
4
comment How can i prove that result on Fibonacci and coprimes?
math.hmc.edu/funfacts/ffiles/20004.5.shtml
May
31
awarded  Talkative
May
29
awarded  Notable Question
May
27
comment Why Circle encloses largest Area?
merci @Pierre-Yves it's clear
May
26
comment Why Circle encloses largest Area?
Could you explain the last equality $\sum_{n\in\mathbb Z}\ n^2\ |c_n|^2=1$?
May
22
suggested suggested edit on Are matrices rank 2 tensors?
May
21
awarded  Supporter
May
4
answered Question on proof of Solutions of Linear Equations