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Let X be a set and S a collection of subsets of X. A subset A subset X is shattered by S if each subset B subset A of A can be expressed as the intersection of A with a ...

The conjecture that all integers >1 occur as a value of the totient valence function (i.e., all integers >1 occur as multiplicities). The conjecture was proved by Ford ...

There appear to be two different definitions of the standard error. The standard error of a sample of sample size n is the sample's standard deviation divided by sqrt(n). It ...

The term "range" has two completely different meanings in statistics. Given order statistics Y_1=min_(j)X_j, Y_2, ..., Y_(N-1), Y_N=max_(j)X_j, the range of the random sample ...

The survival function describes the probability that a variate X takes on a value greater than a number x (Evans et al. 2000, p. 6). The survival function is therefore ...

The weighted mean of a discrete set of numbers {x_1,x_2,...,x_n} with weights {w_1,w_2,...,w_n} is given by <x>=sum_(i=1)^nw_ix_i, (1) where each weight w_i is a nonnegative ...

A matrix whose elements may contain complex numbers. The matrix product of two 2×2 complex matrices is given by (1) where R_(11) = ...

Consider a game, first proposed by Nicolaus Bernoulli, in which a player bets on how many tosses of a coin will be needed before it first turns up heads. The player pays a ...

The asymptotic form of the n-step Bernoulli distribution with parameters p and q=1-p is given by P_n(k) = (n; k)p^kq^(n-k) (1) ∼ 1/(sqrt(2pinpq))e^(-(k-np)^2/(2npq)) (2) ...

The difference between the measured or inferred value of a quantity x_0 and its actual value x, given by Deltax=x_0-x (sometimes with the absolute value taken) is called the ...