Show $E(X)= \int_{[0, \infty)} P[X>t] dt$, without using density argument
38324
Show that $E(X)=\int_{0}^{\infty}P(X\ge x)\,dx$ for non-negative random variable $X$
64856
Finding $E(X\mid X>Y)$ when $X,Y$ are i.i.d $U(0,1)$
14764
Explain why $E(X) = \int_0^\infty (1-F_X (t)) \, dt$ for every nonnegative random variable $X$
81057
Evaluation of $\int_{\frac{1}{e}}^{\tan x}\frac{t}{1+t^2}dt+\int_{\frac{1}{e}}^{\cot x}\frac{1}{t(1+t^2)}dt$
144146
find a $\int_{x}^{g(x)} f(t)\,dt = 1$
61133
Show that $\int|f(x)|dx=\int_0^\infty m(E_\alpha)d\alpha$
43538
Show $\lim_{n \to \infty} n^{-1} E \left( \frac{1}{X}1_{[X>n^{-1}]} \right) =0$
129892
show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
93759
Evaluate $\int_{0}^{\infty} \frac{e^{ax}-e^{bx}}{(1+e^{ax})(1+e^{bx})} dx$
156901
Showing that $X\sim E[X\mid\mathcal{G}]$ implies $X=E[X\mid\mathcal{G}]$ almost surely
27705
Proof of $\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s)$
85311
Proving that $e^{\pi}-{\pi}^e\lt 1$ without using a calculator
139742
Bounding the integral $\int_{2}^{x} \frac{\mathrm dt}{\log^{n}{t}}$
83703
Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $
102286
Compute $\mathbb{P}\{ W_t < 0 \, \, \text{for all} \, \, 1 < t < 2\}$ for a Brownian motion $(W_t)_{t \geq 0}$
79794
Prove the time inversion formula is brownian motion
132920
Help with proof that the expected value of $x_i$ is $\bar{X}$