Let $p>0$ be a constant. Prove that if $E{|X|}^p x)\to 0(x\to \infty)$.
133257
Find limit of a random variable: $\lim_\limits{s\to\infty} s^n P(|Y| > s)$.
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
35325
Prove that $\lim_{n\to\infty}\frac1{n}\int_0^{n}xf(x)dx=0$.
27511
Prove that $\lim_{x \to \infty} \frac{\log(1+e^x)}{x} = 1$
52380
How to prove the function $e^x$ is continous for all real numbers
5350
Explain why $E(|X|^p)=p\int_{0}^{\infty}y^{p-1}P(|X|>y) dy$
35277
Why is $\mathbb{E}[X] = 1 + \sum^\infty_{k=1}\mathbb{P}(X > k)$ true?
142785
How can I prove Holder inequality for $0<p<1$?
121771
Proof $f(x)\equiv 0$
25775
How to prove $(1+1/x)^x$ is increasing when $x>0$?
52545
Prove limit converges in definition of $e.$
56127
Prove a function is constant under certain conditions
37015
Prove $\int_X |f|^p=p\int^{\infty}_{0} t^{p-1}\mu({x: |f(x)>t}) dt\,$
20404
Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$
82204
Prove $ \lim_{n\to\infty}\sqrt[n]{p(n)}=1 $ for polynomial
150896
Show that $\lim_{p \to \infty} \| f \|_p = \| f \|_\infty$
112285
Show that $\lim_{x\to\infty} f(x)=0 \implies \lim_{x\to\infty} f'(x)=0$