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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 ...

The hazard function (also known as the failure rate, hazard rate, or force of mortality) h(x) is the ratio of the probability density function P(x) to the survival function ...

A random number is a number chosen as if by chance from some specified distribution such that selection of a large set of these numbers reproduces the underlying ...

A random number which lies within a specified range (which can, without loss of generality, be taken as [0, 1]), with a uniform distribution.

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 ...

An experiment in which s trials are made of an event, with probability p of success in any given trial.

A time series x_1, x_2, ... is nonstationary if, for some m, the joint probability distribution of x_i, x_(i+1), ..., x_(i+m-1) is dependent on the time index i.

Poisson's theorem gives the estimate (n!)/(k!(n-k)!)p^kq^(n-k)∼e^(-np)((np)^k)/(k!) for the probability of an event occurring k times in n trials with n>>1, p<<1, and np ...

Consider (1) If the probability distribution is governed by a Markov process, then P_3(y_1,t_1;y_2,t_2|y_3,t_3) = P_2(y_2,t_2|y_3,t_3) (2) = P_2(y_2|y_3,t_3-t_2). (3) ...

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 ...