Show $P(X > x) = e^{-\lambda x} \forall x > 0$ and some $\lambda > 0$
14079
On the proof that every positive continuous random variable with the memoryless property is exponentially distributed
151400
Closed-form of $\int_0^1 \operatorname{Li}_p(x) \, dx$
26833
Prove that $\mathbb P(X>Y) =\frac{b}{a + b}$ if $X, Y$ are exponentially distributed with parameters $a$ and $b$.
138962
$X$ is a random variable, if $\Bbb E(X^2)=1$ and $\Bbb E(X)\geq a>0$, prove that $\Bbb P(X\geq\lambda a)\geq(a-\lambda a)^2$ for $0\leq\lambda\leq 1$.
106979
Prove the inequality and limitation
101792
By expanding $e^x$ into a series prove the following inequality
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 $p$
100968
Why is $|e^{i \lambda z}| |e^{- \lambda y}|= |e^{- \lambda y}|$ here?
49061
Show that $\int_{\partial P}z\frac {f'(z)} {f(z)} dz $ is on the lattice $\Lambda$
42193
Show that $E(Y^p)=\int_{0}^{\infty}px^{p-1}P(Y\geq x)dx$
37055
Show that $\lim _{r \to 0} \|T_rf−f\|_{L_p} =0.$
132920
Help with proof that the expected value of $x_i$ is $\bar{X}$
65534
Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
25618
$x,y,z$ independent and uniform random on $[0,1]$, $P(x \geq  yz)$?
90796
Inequality Regarding e
64239
Upper Bound for $p(1-p) $ where $0 \le p \le 1$
117533
$|A-\lambda I|$ and $|\lambda I-A|$