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Experimental mathematics. Experimental mathematics is an approach to mathematics in which computation is used to investigate mathematical objects and identify properties and patterns. [1] It has been defined as "that branch of mathematics that concerns itself ultimately with the codification and transmission of insights within the mathematical ...
Design of experiments. The design of experiments (DOE or DOX), also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design ...
Mathematics in psychology is used extensively roughly in two areas: one is the mathematical modeling of psychological theories and experimental phenomena, which leads to mathematical psychology; the other is the statistical approach of quantitative measurement practices in psychology, which leads to psychometrics. [2]
Replication (statistics) In engineering, science, and statistics, replication is the process of repeating a study or experiment under the same or similar conditions to support the original claim, which crucial to confirm the accuracy of results as well as for identifying and correcting the flaws in the original experiment. [1]
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study ...
e. In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. [1] An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one. A random experiment that has exactly two ...
Then P(n) is true for all natural numbers n. For example, we can prove by induction that all positive integers of the form 2n − 1 are odd. Let P(n) represent " 2n − 1 is odd": (i) For n = 1, 2n − 1 = 2 (1) − 1 = 1, and 1 is odd, since it leaves a remainder of 1 when divided by 2. Thus P(1) is true.
v. t. e. In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3 ...