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Let $Phi$ be the CDF of the normal distribution, and let $u,v,ssimmathrm{Unif}[0,1]$ be iid uniform variables, then $X_1:= Phi^{-1}(u),Y_1:= Phi^{-1}(v)$ will be independent normal variables, therefore ...
1Mathematics Asked on 2 years ago
Suppose you have a quotient of form, $$ frac{ f(x) + g(x) + h(x) + cdots}{ q(x) + r(x) + p(x)+cdots}$$ Consider an expression of sort, $$ lim_{x...
3Mathematics Asked on 2 years ago
For probability triple $(mathbb{R}, mathcal{B}(mathbb{R}), mu)$ prove that for a random variable $X$, if $mu(X>0)>0$, there must be $alpha>0$ s.t. $mu(X>alpha)>0$. So if $X$...
2Mathematics Asked on 2 years ago
Prove or disprove that if $$prodlimits_{x=2}^{infty} f(x)=0$$ and $f(x)neq0$ for any $xgeq0$ then $$prodlimits_{x=2}^{infty} f(xvarphi)=0$$ for any constant $varphigeq2$ This seems true but I'm not...
3Mathematics Asked by Smorx on 2 years ago
The motivation is an object which generalizes the notion of percentages. Consider the the set $mathbb{R}$ along with the usual binary addition operation $+$ and infinitely-many binary multiplication...
0Mathematics Asked on 2 years ago
A diameter $AB$ and a chord $CD$ of a circle $k$ intersect at $M.$ $CE$ and $DF$ are perpendiculars from $C$ and ...
1Mathematics Asked on 2 years ago
In an $atimes b$ board, two players take turns putting a mark on an empty square. Whoever gets $cleq max(a,b)$ consecutive marks horizontally, vertically, or diagonally first wins....
1Mathematics Asked on 2 years ago
I don’t know why contravariant and covariant vector field are named as such. contravariant literally means going against changing, or changing in the opposite way, covariant literally means changing with...
1Mathematics Asked on 2 years ago
Consider a mapbegin{align}F:&[0~1]^mathbb{N}rightarrow mathbb{R}^mathbb{N}\&{x_k}rightarrow {y_k}=F{x_k}end{align}with the following properties:${y_k} rightarrow 0$ for all ${x_k}in[0~1]^mathbb{N}$$y_k=f(y_{k-1},x_k)$ for all $kinmathbb{N}$, where $f(cdot,cdot)$ is...
0Mathematics Asked by Daniel Huff on 2 years ago
I was learning the Krull-Schmidt theory and came across this concept and just can't understand what's it all about. A group endomorphism $fcolon Gto G$ is called normal iff...
2Mathematics Asked by DarkGlimmer on 2 years ago
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