query: Show that $\mathrm{Cov}[g(X), h(X)] \ge 0$ whenever $g$ and $h$ are nondecreasing.
positive_passages.docid: 6450
positive_passages.text: Show $\mathbb{E}[f(X)g(X)] \geq \mathbb{E}[f(X)]\mathbb{E}[g(X)]$ for $f,g$ bounded, nondecreasing
negative_passages.docid: 3296
negative_passages.text: Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
negative_passages.docid: 79826
negative_passages.text: $gHg^{-1}\subset H$ whenever $Ha\not = Hb$ implies $aH\not =bH$
negative_passages.docid: 154612
negative_passages.text: $\int_{0}^{x} f(t) dt \ge {f(x)}$ holds or not on $[0,1]$
negative_passages.docid: 20581
negative_passages.text: How to show that $\Gamma\vdash (\varphi\to\neg\varphi)\to\varphi$?
negative_passages.docid: 76292
negative_passages.text: Showing that $f$ is identically $0$ on $\mathbb{D}$
negative_passages.docid: 157426
negative_passages.text: Proving that:$\int_X f_n g \, d\mu \to \int_X fg \, d\mu$ for all $g$ in $\mathscr{L}^q (X)$
negative_passages.docid: 120985
negative_passages.text: Prove that $\mathrm{Res}[f/g,z_0]=\frac{f(z_0)}{g'(z_0)}$
negative_passages.docid: 150141
negative_passages.text: Showing $X$, $Y$ are not independent but $\operatorname{Cov}[X, Y] = 0$
negative_passages.docid: 11082
negative_passages.text: Borel-Cantelli Lemma "Corollary" in Royden and Fitzpatrick
negative_passages.docid: 95684
negative_passages.text: Show that $g'(x)+g(x)-2e^x=0$
negative_passages.docid: 66531
negative_passages.text: $\|h(x)-h(y)\|\geq 3\|x-y\|$ prove that image of open is open
negative_passages.docid: 106585
negative_passages.text: Show $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$.
negative_passages.docid: 21881
negative_passages.text: Prove that $\forall\alpha\geq\omega$, $|L_\alpha|=|\alpha|$ without AC
negative_passages.docid: 108785
negative_passages.text: Generalized Second Borel-Cantelli lemma
negative_passages.docid: 48563
negative_passages.text: If $\Gamma^k_{ij}(p)=0$, then $\nabla_{E_i}E_j (p)=0?$
negative_passages.docid: 3870
negative_passages.text: A variation of Borel Cantelli Lemma