Probability inequality for the case $E(X^2)=1$
98662
$P(|X|\ge\lambda a)\ge (1-\lambda)^2a^2$ for $0\le \lambda \le 1$
86635
Optimizing $(X_{n}+c)^{2}$ to show that $P(\overline{X}_{n}\geq \lambda) \leq E(X_{n}^{2})/(EX_{n}^{2}+ \lambda^{2})$
52353
Bounding Euler's e by showing $2 \leq \left (1+ \frac{1}{n}\right)^n < 3$
83464
Conditional expectation of $\mathbb{E}(X - Y | (X, Y)\in\mathcal{A})$
20075
Probabilistic method Kraft-McMillan inequality
113411
If $E$ is generated by $E_1$ and $E_2$, then $[E:F]\leq [E_1:F][E_2:F]$?
95123
General solution of expected value of E(f(X))?
102286
Compute $\mathbb{P}\{ W_t < 0 \, \, \text{for all} \, \, 1 < t < 2\}$ for a Brownian motion $(W_t)_{t \geq 0}$
62605
How to find $\mathbb{E}(X\mid\mathbf{1}_{X<Y})$ where $X,Y$ are i.i.d exponential variables?
101792
By expanding $e^x$ into a series prove the following inequality
91131
Question regarding an inequality
25654
E[X| X>Y] for independent X, Y ~ N(0,1)
99024
Let $\,E=\{(x,y) \in \Bbb R^2: |x| \le 1,|y|\le 1\}.$
156599
Wirtinger Inequality: $\int_0^1 f'^2 \geq \pi^2 \int_0^1 f^2 $
92569
Showing that ${\rm E}[X]=\sum_{k=0}^\infty P(X>k)$ for a discrete random variable
95022
Help understanding proof of the following statement $E(Y) = \sum_{i = 1}^{\infty} P(Y \geq k)$
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$