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The Zipf distribution, sometimes referred to as the zeta distribution, is a discrete distribution commonly used in linguistics, insurance, and the modelling of rare events. ...

Let X_1,X_2,...,X_N be a set of N independent random variates and each X_i have an arbitrary probability distribution P(x_1,...,x_N) with mean mu_i and a finite variance ...

If Y_i have normal independent distributions with mean 0 and variance 1, then chi^2=sum_(i=1)^rY_i^2 (1) is distributed as chi^2 with r degrees of freedom. This makes a chi^2 ...

The Bernoulli distribution is a discrete distribution having two possible outcomes labelled by n=0 and n=1 in which n=1 ("success") occurs with probability p and n=0 ...

The quantity twelve (12) is sometimes known as a dozen. It is in turn one twelfth of a gross. Base-12 is known as duodecimal. The Schoolhouse Rock segment "Little Twelvetoes" ...

A 30-60-90 triangle is a right triangle having angles of 30 degrees, 60 degrees, and 90 degrees. For a 30-60-90 triangle with hypotenuse of length a, the legs have lengths b ...

The triangle with edge lengths 3, 4, and 5 is the right triangle with smallest possible integer lengths and corresponds to the Pythagorean triple (3,4,5) where the legs have ...

Let X be an alphabet (i.e., a finite and nonempty set), and call its member letters. A word on X is a finite sequence of letters a_1...a_n, where a_1,...,a_n in X. Denote the ...

A bar (also called an overbar) is a horizontal line written above a mathematical symbol to give it some special meaning. If the bar is placed over a single symbol, as in x^_ ...

The binary logarithm log_2x is the logarithm to base 2. The notation lgx is sometimes used to denote this function in number theoretic literature. However, because Russian ...