query: Closed-form solution for an integral involving the p.d.f. and c.d.f. of a $N(0, 1)$-distributed random variable
positive_passages.docid: 177
positive_passages.text: How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$
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: 41100
negative_passages.text: Density of sum of two independent uniform random variables on $[0,1]$
negative_passages.docid: 90245
negative_passages.text: Computing $\int^1_0 \frac{p^2-1}{\text{ln } p}dp$
negative_passages.docid: 77774
negative_passages.text: Distribution of sums and differences of n correlated normal random variables
negative_passages.docid: 105494
negative_passages.text: Gaussian-like integral : $\int_0^{\infty} e^{-x^2} \cos( a x) \ \mathrm{d}x$
negative_passages.docid: 108560
negative_passages.text: Proof of a Gaussian Integral property
negative_passages.docid: 37192
negative_passages.text: proof of the second generalized mean value theorem for integrals
negative_passages.docid: 14764
negative_passages.text: Explain why $E(X) = \int_0^\infty (1-F_X (t)) \, dt$ for every nonnegative random variable $X$
negative_passages.docid: 72379
negative_passages.text: Convergence of Poisson random variables with divergent parameter
negative_passages.docid: 21857
negative_passages.text: Seeking methods to solve: $\int_0^\infty \frac{\ln(t)}{t^n + 1}\:dt$
negative_passages.docid: 149320
negative_passages.text: Proving an integral formula containing the Poisson kernel
negative_passages.docid: 101045
negative_passages.text: Is there a closed form for the integral $\int_0^1 x^n \log^m (1-x) \, {\rm d}x$?
negative_passages.docid: 129829
negative_passages.text: Integral of Schwartz function over probability measure
negative_passages.docid: 5537
negative_passages.text: Closed form for $ \int_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$
negative_passages.docid: 158932
negative_passages.text: Finding the expected value of a continuous random variable with a polynomial function. Update finding the integral.
negative_passages.docid: 88708
negative_passages.text: An integration of product $(1-x^n)$