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t. e. In probability theory, a probability space or a probability triple is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models the throwing of a die. A probability space consists of three elements: [1][2] A sample space, Ω {\displaystyle \Omega }
In probability theory particularly in the Malliavin calculus, a Gaussian probability space is a probability space together with a Hilbert space of mean zero, ...
The product of two standard probability spaces is a standard probability space. The same holds for the product of countably many spaces, see (Rokhlin 1952, Sect. 3.4), (Haezendonck 1973, Proposition 12), and (Itô 1984, Theorem 2.4.3). A measurable subset of a standard probability space is a standard probability space.
Eidetic memory. Eidetic memory (/ aɪˈdɛtɪk / eye-DET-ik), also known as photographic memory and total recall, is the ability to recall an image from memory with high precision—at least for a brief period of time—after seeing it only once [1] and without using a mnemonic device. [2]
The probability that 100 randomly typed keys will consist of the first 99 digits of pi (including the separator key), or any other particular sequence of that length, is much lower: (1/90) 100. If the monkey's allotted length of text is infinite, the chance of typing only the digit of pi is 0, which is just as possible (mathematically probable ...
In mathematics, Gaussian measure is a Borel measure on finite-dimensional Euclidean space , closely related to the normal distribution in statistics. There is also a generalization to infinite-dimensional spaces. Gaussian measures are named after the German mathematician Carl Friedrich Gauss. One reason why Gaussian measures are so ubiquitous ...
Random counting measure. A random measure of the form: where is the Dirac measure, and are random variables, is called a point process [1][2] or random counting measure. This random measure describes the set of N particles, whose locations are given by the (generally vector valued) random variables . The diffuse component is null for a counting ...
This is the same as saying that the probability of event {1,2,3,4,6} is 5/6. This event encompasses the possibility of any number except five being rolled. The mutually exclusive event {5} has a probability of 1/6, and the event {1,2,3,4,5,6} has a probability of 1, that is, absolute certainty.