All Questions

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Variance of a function of independent random variables

Suppose I have two discrete independant random variables $X$ and $Y$, and that I'm interested in the expected value of the random variable $W$, where: $$W= \text{sign}(X-Y).$$ So, W is 1 if $X>Y$,...
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Proof of characterization of splitting fields

I'm trying to prove that if $K$ is a finite field extension of $F$ such that $K$ is the splitting field of some collection $C$ of polynomials in $F[x]$, then every irreducible polynomial in $F[x]$ ...
175 views

Derivable doesn't exist in english?

I have a question about terminology. See this is what happens: someone says "this function is derivable", and then another, more experienced Anglo-Saxon mathematician goes on to correct this someone, ...
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Function with 2 outputs

I have written the following code: function [ z,a ] = complx( numb ) z=abs(numb); a=angle(numb); end but I get back just z and not a
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uniform continuity of the function $t\mapsto\langle x^*,f(t)\rangle$

Let $X$ be a Banach space. $f:\mathbb{R}\to X$ a function. If we have $t\mapsto\langle x^*,f(t)\rangle$ uniformly continuous on $\mathbb{R}$ for each $x^*\in D$ where $D$ is a dense subset of $X^*$ (...
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Solve a special differential equation

How can I rigorously solve this differential equation ? $$\frac{dy}{dx}=a y^{-1/6}$$ I know how to solve linear ODEs but I don't know how to do it with this one.
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Lie groups. How to show that the group operations are smooth.

$N:=\{g\in GL(n,R) : g_{ij}=0 \forall j>i , g_{ii}=1 ∀i\}$. For this matrix group, how can we show that it is a Lie group? I am at the beginning of the subject of Lie groups so I can not ...