Prove $E((X+Y)^p)\leq 2^p (E(X^p)+E(Y^p))$ for nonnegative random variables $X,Y$ and $p\ge0$
77493
Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
149792
Show that $\lim_{p \to 0} \mathbb {E} [(X^p-1)/p ] = \mathbb{E} [\log X]$
45918
Inequality: $x^2+y^2+xy\ge 0$
40420
Proof by induction of Bernoulli's inequality: $(1 + x)^n \geq 1 + nx$
125707
A simple proof (hopefully) for $2^x \neq 0$
45555
$(x+y)^c\le x^c+y^c$ for $0<c\le1$
108704
Help with proof of $|x+y| \geq |x|-|y|$
152495
Prove that if $X$ and $Y$ are Normal and independent random variables, $X+Y$ and $X-Y$ are independent
45143
Identify $E(X\mid X+Y)$ for $X$ and $Y$ independent and Poisson
117262
Proving a logarithm inequality
64239
Upper Bound for $p(1-p) $ where $0 \le p \le 1$
30386
Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
72735
Understanding the proof of a formula for $p^e\Vert n!$
136694
Probabilistic Proof of Kraft-Mcmillan Inequality
66089
Using AM-GM to prove $\lim_{p\to 0}$ of the $p$-mean is equal to the GM.
88328
Proof of $1+x\leq e^x$ for all x?
25419
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$