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Apr
14
revised How would you use Fubini's theorem to solve $\int_{0}^{1}\int_{\arcsin(y)}^{\frac{\pi}{2}} e^{\cos(x)} \, dx \, dy$
added 4 characters in body; edited title
Apr
14
comment Covering Space of Orthogonal Group
An unexplained downvote happened here. This is cowardice and dishonesty. That should be pointed out more often. ${}\qquad{}$
Apr
14
revised How is this identical transformation true $x^{1-\log(x)}=1\Longleftrightarrow \log x^{1-\log(x)}=\log1$?
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Apr
14
revised How is this identical transformation true $x^{1-\log(x)}=1\Longleftrightarrow \log x^{1-\log(x)}=\log1$?
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Apr
14
answered Covering Space of Orthogonal Group
Apr
14
comment Covering Space of Orthogonal Group
A manifold can have more than one covering space, but all of them are quotients of a universal covering space, whose fundamental group is trivial (i.e. it is simply connected). ${}\qquad{}$
Apr
14
comment Covering Space of Orthogonal Group
Questions here should generally not be phrased in a manner suitable for assigning homework, and that is probably why somebody down-voted it.
Apr
14
answered All sets of rational numbers are bigger than the set containing infinite integers - or are they?
Apr
14
comment Terms needed to approximate with given error?
I wrote an earlier version of this with $9999$ as the smallest index considered and then revised it, but maybe that was hasty too.
Apr
14
comment Expectation of product of two correlated gaussian variables
@wolfies : $\operatorname{cov}(X_D+G,Y_D+G)$ $=\operatorname{cov}(X_D,Y_D)+\operatorname{cov}(X_D,G)+\operatorname{cov}(Y_D,G‌​)+\operatorname{var}(G)$. Three of these terms are zero; the fourth is not; hence the covariance is not zero and so neither is the correlation. ${}\qquad{}$
Apr
14
comment Terms needed to approximate with given error?
As I said, haste makes waste$\ldots\ldots$ ${}\qquad{}$
Apr
14
revised Terms needed to approximate with given error?
added 17 characters in body
Apr
14
comment Terms needed to approximate with given error?
ok, I hope I've fixed these details$\ldots\ldots$ ${}\qquad{}$
Apr
14
revised Terms needed to approximate with given error?
edited body
Apr
14
comment Terms needed to approximate with given error?
sigh..... Haste makes waste.....
Apr
14
answered Expectation of product of two correlated gaussian variables
Apr
14
comment Expectation of product of two correlated gaussian variables
Your notation hints that you want $X$ to be the sum of two random variables and $Y$ to be the sum of two random variables, where the two sums have a term in common. Is that what you intended? Did you want the things you add to that common term to be independent of each other?
Apr
14
comment Expectation of product of two correlated gaussian variables
One thing you have not told us is whether $X,Y$ are jointly Gaussian, i.e. so distributed that every constant linear combination of them is Gaussian. ${}\qquad{}$
Apr
14
revised Expectation of product of two correlated gaussian variables
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Apr
14
answered Banach space it isn't Hilbert space