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Mathematical statistics is the application of probability theory and other mathematical concepts to statistics, as opposed to techniques for collecting statistical data. [1] Specific mathematical techniques that are commonly used in statistics include mathematical analysis , linear algebra , stochastic analysis , differential equations , and ...
A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematical parameters. [ 1 ] [ verification needed ] [ clarification needed ] Often, such games have simple rules and match procedures, such as tic-tac-toe and dots and boxes .
While many scientific investigations make use of data, statistics is generally concerned with the use of data in the context of uncertainty and decision-making in the face of uncertainty. [7] [8] In applying statistics to a problem, it is common practice to start with a population or process to be studied. Populations can be diverse topics ...
Randomization is a statistical process in which a random mechanism is employed to select a sample from a population or assign subjects to different groups. [1] [2] [3] The process is crucial in ensuring the random allocation of experimental units or treatment protocols, thereby minimizing selection bias and enhancing the statistical validity. [4]
In the lower plot, both the area and population data have been transformed using the logarithm function. In statistics, data transformation is the application of a deterministic mathematical function to each point in a data set—that is, each data point z i is replaced with the transformed value y i = f(z i), where f is a function.
A subfield of set theory that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Games studied in set theory are Gale–Stewart games – two-player games of perfect information in which the players make an infinite sequence of moves and there ...
The Mandelbrot set, one of the most famous examples of mathematical visualization.. Mathematical phenomena can be understood and explored via visualization.Classically, this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century).
A Bayesian-Nash Equilibrium of a Bayesian game is a Nash equilibrium of its associated ex-ante normal form game. In a non-Bayesian game, a strategy profile is a Nash equilibrium if every strategy in that profile is a best response to every other strategy in the profile; i.e., there is no strategy that a player could play that would yield a ...