Let $X$ be a non-negative random variable. Show $(EX)(E\frac{1}{X})\geq 1$
64486
Show that for non-negative measurable functions $f,g$ with $fg \geq 1$ the inequality $(\int f^p)(\int g^p) \geq 1$ holds.
30662
$x_{1}...x_{n}$ are independent continuous random variables with common distribution function $F(x)$,compute $E(F(x_{(n)})-F(x_{(1)}))$
118091
Taylor expansion of $\exp(-x)$: proof tail is positive
36417
Why does $\mathbb{E}(\frac{X_1+...+X_n}{n})=\mathbb{E}(X)$?
118195
How does one prove that $e$ exists?
113778
Show that $E=\{(x,\alpha)\mid 0\leq \alpha<|f(x)|\}$ is measurable if $f$ is measurable.
106868
Prove that $x+\frac1{4x} ≥ 1$ for $x>0$
101792
By expanding $e^x$ into a series prove the following inequality
43226
Intuition behind logarithm inequality: $1 - \frac1x \leq \log x \leq x-1$
64493
$X$ is a Geometric random variable find the expectation of $1/X$
64856
Finding $E(X\mid X>Y)$ when $X,Y$ are i.i.d $U(0,1)$
83464
Conditional expectation of $\mathbb{E}(X - Y | (X, Y)\in\mathcal{A})$
24683
For i.i.d. $\{X_n\}$ proving $\frac1n\max\limits_{1\leqslant k\leqslant n}|X_k|\xrightarrow{\mathrm{a.s.}}0\Leftrightarrow E(|X_1|)<+∞$
40420
Proof by induction of Bernoulli's inequality: $(1 + x)^n \geq 1 + nx$
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
109109
Show that $E(XE[X|G])=E[(E[X|G)^2]$
44233
How to prove this inequality $ x + \frac{1}{x} \geq 2 $