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There are a great many beautiful identities involving q-series, some of which follow directly by taking the q-analog of standard combinatorial identities, e.g., the ...

The Gaussian integral, also called the probability integral and closely related to the erf function, is the integral of the one-dimensional Gaussian function over ...

Kurtosis is defined as a normalized form of the fourth central moment mu_4 of a distribution. There are several flavors of kurtosis, the most commonly encountered variety of ...

The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. For a sample size N, the mean ...

The mean line segment length l^_ is the average length of a line segment in line segment picking within some given shape. As summarized in the following table (where Delta(3) ...

Given a function f(x) of a variable x tabulated at m values y_1=f(x_1), ..., y_m=f(x_m), assume the function is of known analytic form depending on n parameters ...

Poker is a card game played with a normal deck of 52 cards. Sometimes, additional cards called "jokers" are also used. In straight or draw poker, each player is normally ...

Given the closed interval [0,x] with x>1, let one-dimensional "cars" of unit length be parked randomly on the interval. The mean number M(x) of cars which can fit (without ...

Let the number of random walks on a d-D hypercubic lattice starting at the origin which never land on the same lattice point twice in n steps be denoted c_d(n). The first few ...

For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as ...