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In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field, where the σ comes from the German "Summe" [1]) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections. The ordered pair (,) is called a measurable space.
A Taylor series is also called a Maclaurin series ... This series can be written by using sigma notation, ... that depends on two variables, x and y, the Taylor ...
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.
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.
In the empirical sciences, the so-called three-sigma rule of thumb (or 3 σ rule) expresses a conventional heuristic that nearly all values are taken to lie within three standard deviations of the mean, and thus it is empirically useful to treat 99.7% probability as near certainty.
also called the magnetic field density or magnetic induction tesla (T), or equivalently, weber per square meter (Wb/m 2) capacitance: farad (F) heat capacity: joule per kelvin (J⋅K −1) constant of integration: varied depending on context speed of light (in vacuum) 299,792,458 meters per second (m/s) speed of sound
The hierarchy includes at present three models, with 1, 2 and 3 parameters, if not counting the maximal number of nuclei N max, respectively—a tanh 2 based model called α 21 [11] originally devised to describe diffusion-limited crystal growth (not aggregation!) in 2D, the Johnson-Mehl-Avrami-Kolmogorov (JMAKn) model [12], and the Richards ...
For instance, rearranging the terms of the alternating harmonic series so that each positive term of the original series is followed by two negative terms of the original series rather than just one yields [34] + + + = + + + = + + + = (+ + +), which is times the original series, so it would have a sum of half of the natural logarithm of 2. By ...