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Normal number. In mathematics, a real number is said to be simply normal in an integer base b[1] if its infinite sequence of digits is distributed uniformly in the sense that each of the b digit values has the same natural density 1/ b. A number is said to be normal in base b if, for every positive integer n, all possible strings n digits long ...
Normal (geometry) A polygon and its two normal vectors. A normal to a surface at a point is the same as a normal to the tangent plane to the surface at the same point. In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the ...
Normality test. In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed. More precisely, the tests are a form of model selection, and can be interpreted several ways, depending on one's ...
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a ...
Probability theory. In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while ...
Standard normal table. In statistics, a standard normal table, also called the unit normal table or Z table, [1] is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal ...
In mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A *: =. The concept of normal matrices can be extended to normal operators on infinite-dimensional normed spaces and to normal elements in C*-algebras. As in the matrix case, normality means commutativity is preserved, to the extent possible, in the ...
The scaled sum of a sequence of i.i.d. random variables with finite positive variance converges in distribution to the normal distribution. In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution.