Let $X$ and $Y$ be iid real-valued random variables. Show $P[|X-Y| \le 2] \le 3P[|X-Y| \le 1]$.
46760
To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
122719
Show that random variables $X$ and $Y$ are not independent, but nevertheless Cov$[X,Y] = 0$
81363
How to compute $P(X>Y)$ if $X$ and $Y$ are independent and exponentially distributed
92569
Showing that ${\rm E}[X]=\sum_{k=0}^\infty P(X>k)$ for a discrete random variable
14079
On the proof that every positive continuous random variable with the memoryless property is exponentially distributed
110495
$X_n \to X, Y_n \to c$ in distribution implies $X_n Y_n \to Xc$ in distribution
133801
Finding the PGF of $Z$ using conditional expectation.
14664
Sum of indepedent random variables and a constant
68512
$\sigma$ algebra of collection of random variables
64856
Finding $E(X\mid X>Y)$ when $X,Y$ are i.i.d $U(0,1)$
6190
Maximum/minimum of two random variables is a random variable
7775
Show that $|x-y|\leq |x|+|y|$.
83464
Conditional expectation of $\mathbb{E}(X - Y | (X, Y)\in\mathcal{A})$
54791
Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
119735
Show that $\mathbb{E}(g(T-p)) < \mathbb{E}(g(S-p))$ for any convex function $g$ if $T$ and $S$ are estimators of $p$
117907
A question regarding independence of $\min{\{X,Y\}}$ and $X-Y$ when $X,Y$ follows iid geometric distribution