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I was doing an exercise and I saw this property, I would like to know why it's true. Let $V$ be a $mathbb{K}$-dimensional vector space and Let ...
Asked on 12/06/2020 by Ivan Bravo
2 answerI want to show that $mathbb {E}(mathbb {E}(Xmid mathcal {F}))=mathbb {E}X$. My thought is that begin{align*}mathbb {E}(mathbb {E}(Xmid mathcal {F}))=sum_{Omega_{i}} frac {mathbb {E}(X;Omega_{i})}{mathbb {P}(Omega_{i})}mathbb {P}(Omega_{i})=mathbb{E}X,end{align*}where...
Asked on 12/06/2020 by Jiexiong687691
1 answerFor $z,w in mathbb{C}$ How to show the identity: $$2(|z|^n+|w|^n) leq (|z+w|^n + |z-w|^n )? $$ for $n geq 2$.I tried induction, but can't I finish....
Asked on 12/06/2020 by stranger
1 answerI feel like most definitions of “independence” are circular. Consider how we count the number of cards in a standard deck of cards: $|S times R| = |S||R|$, where...
Asked on 12/06/2020 by trivial math is difficult
3 answerShow that the function $f(z)=frac{1-cos z}{z^n}$ has no anti-derivative on $mathbb Csetminus{0}$ if $n$ is a positive odd integer. I think, If we can able to prove...
Asked on 12/06/2020 by RIYASUDHEEN T. K
1 answerFind all stationary pointsfor function$$f(x,y)=3y^3-x^3-2y^2+4x-2y.$$So far this is what I have$$frac{partial f}{partial x}left(3y^3-x^3-2y^2+4x-2yright)=-3x^2-4$$ and$$frac{partial f}{partial y}left(3y^3-x^3-2y^2+4x-2yright)=9y^2-4y-2$$ What do I do from here? I...
Asked on 12/06/2020 by Mads Peter Balle
1 answerWhile reading a book, I found an example that said that the ring $K[w,x,y,z]/(wy,wz,xy,xz)$ is not Cohen-Macaulay. In order to check this, it is stated to take the quotient...
Asked on 12/06/2020
2 answerLet $a,b,cge 3$ be natural numbers. If $ale ble c$ and $mle nle p$ the following proposition is true? $$a!cdot b!cdot c!=m!cdot n!cdot p!to (a,b,c)=(m,n,p)...
Asked on 12/06/2020 by felipeuni
4 answerConsider a quadratic equation in two variables, $f(x,y) = ax^2 + bxy + cy^2 + d$. Let $P$ be a plane, so it is described by some equation...
Asked on 12/06/2020 by twosigma
0 answerThe question is as is, just proving that $x^2$ is analytic in $mathbb{R}$. Is this just true because for $|x|<1$ we have by the geometric series that...
Asked on 12/05/2020 by Joey
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