query: How to show that $\exp(x+y) = \exp(x)\times\exp(y)$
positive_passages.docid: 32407
positive_passages.text: Prove $\exp(x+y) = \exp(x) \exp(y)$ for $\exp(x) = \sum_{n=0}^\infty \frac {x^n}{n!}$
negative_passages.docid: 109109
negative_passages.text: Show that $E(XE[X|G])=E[(E[X|G)^2]$
negative_passages.docid: 34693
negative_passages.text: Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
negative_passages.docid: 42193
negative_passages.text: Show that $E(Y^p)=\int_{0}^{\infty}px^{p-1}P(Y\geq x)dx$
negative_passages.docid: 64656
negative_passages.text: how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
negative_passages.docid: 92054
negative_passages.text: $X$ and $Y$ i.i.d., $X+Y$ and $X-Y$ independent, $\mathbb{E}(X)=0 $ and $\mathbb{E}(X^2)=1$. Show $X \sim N(0,1)$
negative_passages.docid: 49211
negative_passages.text: Solving $f(x+y) = f(x)f(y)f(xy)$
negative_passages.docid: 2315
negative_passages.text: How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?
negative_passages.docid: 154698
negative_passages.text: Union of Cartesian products: $X \times (Y \cup Z)= (X \times Y) \cup(X\times Z)$
negative_passages.docid: 12083
negative_passages.text: How to prove $\limsup (x_{n}+y_{n})=\lim x_{n}+\limsup y_{n}$?
negative_passages.docid: 129584
negative_passages.text: How prove $E|X|^p<\infty$ and $E|Y|^p<\infty$, if $E|X+Y|^p<\infty$
negative_passages.docid: 120957
negative_passages.text: show that Cov(X+ Y, X-Y)= Var(X) - Var(Y)
negative_passages.docid: 39455
negative_passages.text: Prove that $(X\times Y)\setminus (A\times B)$ is connected
negative_passages.docid: 143765
negative_passages.text: To Show that $\exp(tX)\exp(tY)= \exp(t(X+Y)) + (1/2)t^2[X, Y] +o(t^3)$
negative_passages.docid: 114411
negative_passages.text: Simple Proof of the Euler Identity $\exp{i\theta}=\cos{\theta}+i\sin{\theta}$
negative_passages.docid: 58741
negative_passages.text: Operator Exponential $e^A e^B = e^{A+B}$
negative_passages.docid: 66457
negative_passages.text: Series expansion of $xy'=y$