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Any combination of events using the operations and, or, and not is also an event, and assigning probabilities to all outcomes generates a probability for every event. In technical terms, this means that the set of events and the three operations together constitute a Boolean algebra of sets, with an associated probability function .
In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) [5] and providing an output (which may also be a number). [5] A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. [6]
Microsoft Math Solver (formerly Microsoft Mathematics and Microsoft Math) is an entry-level educational app that solves math and science problems. Developed and maintained by Microsoft, it is primarily targeted at students as a learning tool. Until 2015, it ran on Microsoft Windows.
It was superseded in 2009 by ISO 80000-2:2009 and subsequently revised in 2019 as ISO-80000-2:2019. [1] It included definitions for symbols for mathematical logic, set theory, arithmetic and complex numbers, functions and special functions and values, matrices, vectors, and tensors, coordinate systems, and miscellaneous mathematical relations. [2]
In mathematics, a dependence relation is a binary relation which generalizes the relation of linear dependence.. Let be a set.A (binary) relation between an element of and a subset of is called a dependence relation, written , if it satisfies the following properties:
A tail event is then by definition an event which is measurable with respect to the σ-algebra generated by all X n, but which is independent of any finite number of X n. That is, a tail event is precisely an element of the terminal σ-algebra ⋂ n = 1 ∞ G n {\displaystyle \textstyle {\bigcap _{n=1}^{\infty }G_{n}}} .
In essence probability is influenced by a person's information about the possible occurrence of an event. For example, let the event be 'I have a new phone'; event be 'I have a new watch'; and event be 'I am happy'; and suppose that having either a new phone or a new watch increases the probability of my being happy.
The concepts of dependence and independence of systems are partially generalized in numerical linear algebra by the condition number, which (roughly) measures how close a system of equations is to being dependent (a condition number of infinity is a dependent system, and a system of orthogonal equations is maximally independent and has a ...