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visits member for 2 years, 4 months
seen Jul 18 at 6:15

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
comment partial derivatives of Dirac functions
right, indeed, $\delta = \delta_0$ and $x_i$ is null
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
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
1
comment Normal Distribution Quantiles and Value at Risk
Also, don't smoke
Mar
7
comment What is exponentiation?
isn't $a^{\pi} < max(a^3,a^4)$ enough to say it's convergent (since it's also increasing with your decomposition)
Dec
2
comment Calculate interests
I'm currently googling to know which option is commonly used, thx
Dec
2
comment Calculate interests
yes r: yearly interests of the loan and m: monthly payback, @AndréNicolas I have edited the question with what you suggested can you have a look?
Dec
2
comment Calculate interests
I don't agree, at the end of first year, the loan is N less 12 paybacks, and you add the interests
Dec
2
comment Calculate interests
ok else, to me, for the amount at beginning of years: $N_y = N_{y-1} - 12m + r(N_{y-1}-6m)$ no? (you have put $12m$ also multiplied by r)
Dec
2
comment Calculate interests
seems x and y are mixed, it's V(x,b... ) above?
Dec
2
comment Calculate interests
@AndréNicolas I thought when you do a loan, the interests were added at the end of the year only, but it's probably each months, it would increase slightly the result. yes r is the nominal interest rate (e.g. 2.5%), @ Limitless thx trying to understand it