Random variableA random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.
Random walkIn mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler.
BehaviorBehavior (American English) or behaviour (British English) is the range of actions and mannerisms made by individuals, organisms, systems or artificial entities in some environment. These systems can include other systems or organisms as well as the inanimate physical environment. It is the computed response of the system or organism to various stimuli or inputs, whether internal or external, conscious or subconscious, overt or covert, and voluntary or involuntary.
Consumer behaviourConsumer behaviour is the study of individuals, groups, or organisations and all the activities associated with the purchase, use and disposal of goods and services. Consumer behaviour consists of how the consumer's emotions, attitudes, and preferences affect buying behaviour. Consumer behaviour emerged in the 1940–1950s as a distinct sub-discipline of marketing, but has become an interdisciplinary social science that blends elements from psychology, sociology, social anthropology, anthropology, ethnography, ethnology, marketing, and economics (especially behavioural economics).
RandomnessIn common usage, randomness is the apparent or actual lack of definite pattern or predictability in information. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events (or "trials") is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4.
Algorithmically random sequenceIntuitively, an algorithmically random sequence (or random sequence) is a sequence of binary digits that appears random to any algorithm running on a (prefix-free or not) universal Turing machine. The notion can be applied analogously to sequences on any finite alphabet (e.g. decimal digits). Random sequences are key objects of study in algorithmic information theory. As different types of algorithms are sometimes considered, ranging from algorithms with specific bounds on their running time to algorithms which may ask questions of an oracle machine, there are different notions of randomness.
Behavioural sciencesThe behavioural sciences explore the cognitive processes within organisms and the behavioural interactions between organisms in the natural world. It involves the systematic analysis and investigation of human and animal behaviour through naturalistic observation, controlled scientific experimentation and mathematical modeling. It attempts to accomplish legitimate, objective conclusions through rigorous formulations and observation. Examples of behavioural sciences include psychology, psychobiology, anthropology, economics, and cognitive science.
Random matrixIn probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathematically as matrix problems. For example, the thermal conductivity of a lattice can be computed from the dynamical matrix of the particle-particle interactions within the lattice. In nuclear physics, random matrices were introduced by Eugene Wigner to model the nuclei of heavy atoms.
Moiré patternIn mathematics, physics, and art, moiré patterns (UK'mwɑːɹeɪ , USmwɑːˈɹeɪ , mwaʁe) or moiré fringes are large-scale interference patterns that can be produced when a partially opaque ruled pattern with transparent gaps is overlaid on another similar pattern. For the moiré interference pattern to appear, the two patterns must not be completely identical, but rather displaced, rotated, or have slightly different pitch. Moiré patterns appear in many situations. In printing, the printed pattern of dots can interfere with the image.
Mathematical economicsMathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
