query: Intuitive explanation for $E[X]=\int_{0}^\infty P(X\ge x) dx$
positive_passages.docid: 25652
positive_passages.text: Intuitive explanation for $\mathbb{E}X= \int_0^\infty 1-F(x) \, dx$
negative_passages.docid: 134696
negative_passages.text: How can I show that the conditional expectation $E(X\mid X)=X$?
negative_passages.docid: 39723
negative_passages.text: $\int_2^\infty \left(\frac1{x\log^2x}\right)^p\mathrm dx$ diverges for p>1
negative_passages.docid: 44416
negative_passages.text: Ito integral property
negative_passages.docid: 149362
negative_passages.text: Prove that $ \mathbb{E}[XY] - \mathbb{E}[X] \mathbb{E}[Y] = \int_{- \infty}^\infty \int_{- \infty}^\infty (F(x,y)-F_X(x) F_Y(y)) \,dx\,dy,$
negative_passages.docid: 54244
negative_passages.text: Understanding the Proof of L'Hopital's Rule
negative_passages.docid: 17754
negative_passages.text: Intuitive Understanding of the constant "$e$"
negative_passages.docid: 154612
negative_passages.text: $\int_{0}^{x} f(t) dt \ge {f(x)}$ holds or not on $[0,1]$
negative_passages.docid: 82930
negative_passages.text: Why do we say a probability integral transformed variable is uniform on the interval [0, 1]?
negative_passages.docid: 109109
negative_passages.text: Show that $E(XE[X|G])=E[(E[X|G)^2]$
negative_passages.docid: 156019
negative_passages.text: Expectation formula of an integrable random variable
negative_passages.docid: 80803
negative_passages.text: Conditional expectation $E[\log(1+X) \mid X>t]$
negative_passages.docid: 27788
negative_passages.text: Why is the expected value $E(X^2) \neq E(X)^2$?
negative_passages.docid: 140790
negative_passages.text: Prove that $E(X) = \int_{0}^{\infty} P(X>x)\,dx = \int_{0}^{\infty} (1-F_X(x))\,dx$.
negative_passages.docid: 62510
negative_passages.text: Explanation of linearity of expectation
negative_passages.docid: 147705
negative_passages.text: Show that $\mathbb{E}(T) = \sum\limits^\infty_{k=1}\mathbb{P}(T \geq k)$ for $T$ nonnegative integer valued and $E[T] < \infty$
negative_passages.docid: 21004
negative_passages.text: Formula similar to $EX=\sum\limits_{i=1}^{\infty}P\left(X\geq i\right)$ to compute $E(X^n)$?