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This is the appropriate partial ordering because of such facts as that char(A × B) is the least common multiple of char A and char B, and that no ring homomorphism f : A → B exists unless char B divides char A. The characteristic of a ring R is n precisely if the statement ka = 0 for all a ∈ R implies that k is a multiple of n.
An arbitrary function φ : R n → C is the characteristic function of some random variable if and only if φ is positive definite, continuous at the origin, and if φ(0) = 1. Khinchine’s criterion. A complex-valued, absolutely continuous function φ, with φ(0) = 1, is a characteristic function if and only if it admits the representation
In industrial statistics, the X-bar chart is a type of variable control chart [1] that is used to monitor the arithmetic means of successive samples of constant size, n. This type of control chart is used for characteristics that can be measured on a continuous scale, such as weight, temperature, thickness etc.
A subgroup H of a group G is called a characteristic subgroup if for every automorphism φ of G, one has φ(H) ≤ H; then write H char G. It would be equivalent to require the stronger condition φ(H) = H for every automorphism φ of G, because φ −1 (H) ≤ H implies the reverse inclusion H ≤ φ(H).
Random variables are usually written in upper case Roman letters, such as or and so on. Random variables, in this context, usually refer to something in words, such as "the height of a subject" for a continuous variable, or "the number of cars in the school car park" for a discrete variable, or "the colour of the next bicycle" for a categorical variable.
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The character: of a representation: of a group G on a finite-dimensional vector space V over a field F is the trace of the representation (), i.e. = (()) for In general, the trace is not a group homomorphism, nor does the set of traces form a group.
In statistical process control (SPC), the ¯ and R chart is a type of scheme, popularly known as control chart, used to monitor the mean and range of a normally distributed variables simultaneously, when samples are collected at regular intervals from a business or industrial process. [1]