query: How to prove $E(Y|X)=E(Y),a.s.$ formally if $X,Y$ are independent?
positive_passages.docid: 26369
positive_passages.text: Proving seemingly obvious equations with measure theory
negative_passages.docid: 20750
negative_passages.text: Proving an equality regarding fully independent events
negative_passages.docid: 121853
negative_passages.text: $X$,$Y$,$Z$ mutually independent implies $X+Y$ independent of $Z$
negative_passages.docid: 39378
negative_passages.text: Moment generating functions/ Characteristic functions of $X,Y$ factor implies $X,Y$ independent.
negative_passages.docid: 33054
negative_passages.text: Given a joint density function, what is the conditional expectation $E[Y|x]$?
negative_passages.docid: 133228
negative_passages.text: Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
negative_passages.docid: 152495
negative_passages.text: Prove that if $X$ and $Y$ are Normal and independent random variables, $X+Y$ and $X-Y$ are independent
negative_passages.docid: 108704
negative_passages.text: Help with proof of $|x+y| \geq |x|-|y|$
negative_passages.docid: 94077
negative_passages.text: Proof of linear independence of $e^{at}$
negative_passages.docid: 19973
negative_passages.text: If $X$ and $Y$ are independent $N(0,\sigma^2)$, then $X^2+Y^2$ and $X/Y$ are independent?
negative_passages.docid: 38785
negative_passages.text: Prove previsibility and $E[X_{T \wedge n}] \le E[X_{S \wedge n}]$
negative_passages.docid: 29679
negative_passages.text: Prove: $|x-y|\leq |x|+|y|$
negative_passages.docid: 133833
negative_passages.text: If $E(Y\mid X)$ is constant then $X, Y$ are uncorrelated.
negative_passages.docid: 9665
negative_passages.text: Proof of the independence of the sample mean and sample variance
negative_passages.docid: 149362
negative_passages.text: Prove that $ \mathbb{E}[XY] - \mathbb{E}[X] \mathbb{E}[Y] = \int_{- \infty}^\infty \int_{- \infty}^\infty (F(x,y)-F_X(x) F_Y(y)) \,dx\,dy,$
negative_passages.docid: 62605
negative_passages.text: How to find $\mathbb{E}(X\mid\mathbf{1}_{X<Y})$ where $X,Y$ are i.i.d exponential variables?
negative_passages.docid: 15354
negative_passages.text: Formal proof of $\exists x \forall y P(x,y) \implies \forall y \exists x P(x,y)$