query: On Pr(X>Y) when X and Y are independent normal
positive_passages.docid: 154309
positive_passages.text: Probability question of independent random varaibles
negative_passages.docid: 95084
negative_passages.text: What is the expected value of $\min\{|X|,|Y|\}/\max\{|X|,|Y|\}$ assuming $X$ and $Y$ are independent?
negative_passages.docid: 88860
negative_passages.text: The product of two lognormal random variables
negative_passages.docid: 28878
negative_passages.text: Convex function of independent vs. correlated random variables redux
negative_passages.docid: 128558
negative_passages.text: Inequality between $\ell^p$-norms
negative_passages.docid: 52395
negative_passages.text: Distribution of Product of Random Variables with one being the normal distribution.
negative_passages.docid: 68137
negative_passages.text: Independence and conditional independence between random variables
negative_passages.docid: 36374
negative_passages.text: Exercise 1.6.3 from Alon & Spencer's *The Probabilistic Method*: prove that $Pr[|X-Y| \leq 2] \leq 3 Pr[|X-Y| \leq 1]$ for i.i.d. real RVs $X$ and $Y$
negative_passages.docid: 150141
negative_passages.text: Showing $X$, $Y$ are not independent but $\operatorname{Cov}[X, Y] = 0$
negative_passages.docid: 62053
negative_passages.text: If $X$ and $Y$ are independent Normal variables each with mean zero, then $\frac{XY}{\sqrt{X^2+Y^2}}$ is also a Normal variable
negative_passages.docid: 156965
negative_passages.text: Expected value of $\max\{X,Y\}$ when $(X,Y)$ is bivariate normal
negative_passages.docid: 113255
negative_passages.text: $X,Y\sim U(0,1)$ are independent, $W=\max (X,Y)$.
negative_passages.docid: 13831
negative_passages.text: Find $ P(Z>X+Y)$ where $X,Y,Z \sim U(0,1)$ independently
negative_passages.docid: 105125
negative_passages.text: If $X, Y$ are jointly standard normal with correlation $r$, and $a, b$ are constants, what is $p(Y < b | X < a)$?
negative_passages.docid: 105850
negative_passages.text: Compute $E(X\mid X+Y)$ for independent random variables $X$ and $Y$ with standard exponential distributions
negative_passages.docid: 87199
negative_passages.text: Normal distribution tail probability inequality
negative_passages.docid: 26740
negative_passages.text: Showing that asymptotic normality implies consistency.