query: How do I prove that $ E[X] = \int _{0}^\infty (1-F_x(t))dt $
positive_passages.docid: 22085
positive_passages.text: Expectation of a function of a random variable from CDF
negative_passages.docid: 98836
negative_passages.text: Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$
negative_passages.docid: 10408
negative_passages.text: Uniformly convergence of $f_{n+1}(x)= \int^x_0 f_n(t)dt$
negative_passages.docid: 62192
negative_passages.text: Proof $L{\rm{[}}\frac{{x(t)}}{t}{\rm{] = }}\int_s^\infty {X(u)du} $
negative_passages.docid: 87149
negative_passages.text: Prove directly from the definition of the Ito's integral
negative_passages.docid: 52545
negative_passages.text: Prove limit converges in definition of $e.$
negative_passages.docid: 104853
negative_passages.text: Proving that $\lim\limits_{n\to\infty}n\left( \int_0^1 f(t)\, dt -\frac1n\sum_{k=0}^{n-1}f\left(\frac k n\right) \right)=\frac{f(1)-f(0)}{2}$
negative_passages.docid: 38324
negative_passages.text: Show that $E(X)=\int_{0}^{\infty}P(X\ge x)\,dx$ for non-negative random variable $X$
negative_passages.docid: 151127
negative_passages.text: Confirm that $\int_{0}^{\infty}t^{-1}\sin t dt=\pi/2$
negative_passages.docid: 4656
negative_passages.text: Prove that there is a $\delta$ such that $\int_{0}^{1} (f(x))^2dx\leq \delta$$\int_{0}^{1} (f'(x))^2dx$ for all $f$ with these conditions
negative_passages.docid: 101267
negative_passages.text: Show: $\int f\, d\mu=\int\limits_0^{\infty}\mu(\left\{x\in X: f(x)>t\right\})\, dt$
negative_passages.docid: 107987
negative_passages.text: How do I calculate $u(w)=\int_0^\infty \frac{1-\cos(wt)}{t}\,e^{-t}\,dt$?
negative_passages.docid: 7384
negative_passages.text: How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
negative_passages.docid: 124463
negative_passages.text: Integral from $0$ to $\infty$ of $\ln(x)/e^x$
negative_passages.docid: 113141
negative_passages.text: Prove that $\lim_{n \to \infty}\bigg[\int_0^1f(t)^n \text{dt}\bigg]^{1/n}=M$
negative_passages.docid: 95022
negative_passages.text: Help understanding proof of the following statement $E(Y) = \sum_{i = 1}^{\infty} P(Y \geq k)$
negative_passages.docid: 21857
negative_passages.text: Seeking methods to solve: $\int_0^\infty \frac{\ln(t)}{t^n + 1}\:dt$