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Given a regular pentagon of unit area, mean triangle area of a triangle picked at random inside it is given by the n=5 case of polygon triangle picking, A^_ = ...

Erdős and Rényi (1960) showed that for many monotone-increasing properties of random graphs, graphs of a size slightly less than a certain threshold are very unlikely to have ...

Consider a bivariate normal distribution in variables x and y with covariance rho=rho_(11)=<xy>-<x><y> (1) and an arbitrary function g(x,y). Then the expected value of the ...

Given a random variable X with continuous and strictly monotonic probability density function f(X), a quantile function Q_f assigns to each probability p attained by f the ...

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

Pick two real numbers x and y at random in (0,1) with a uniform distribution. What is the probability P_(even) that [x/y], where [r] denotes the nearest integer function, is ...

The Robbins constant is the mean line segment length, i.e., the expected distance between two points chosen at random in cube line picking, namely Delta(3) = (1) = (2) = ...

For two random variates X and Y, the correlation is defined bY cor(X,Y)=(cov(X,Y))/(sigma_Xsigma_Y), (1) where sigma_X denotes standard deviation and cov(X,Y) is the ...

The Wiener sausage of radius a>0 is the random process defined by W^a(t)= union _(0<=s<=t)B_a(beta(s)) where here, beta(t) is the standard Brownian motion in R^d for t>=0 and ...

Cube point picking is the three-dimensional case of hypercube point picking. The average distance from a point picked at random inside a unit cube to the center is given by ...