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Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
Any conditional statement consists of at least one sufficient condition and at least one necessary condition. In data analytics , necessity and sufficiency can refer to different causal logics, [ 7 ] where necessary condition analysis and qualitative comparative analysis can be used as analytical techniques for examining necessity and ...
Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
However, note that performance suffers when there are more than 100 alternatives. Placing common values earlier in the list of cases can cause the function to execute significantly faster. For each case, either side of the equals sign "=" can be a simple string, a call to a parser function (including #expr to evaulate expressions), or a ...
If the conditional distribution of given is a continuous distribution, then its probability density function is known as the conditional density function. [1] The properties of a conditional distribution, such as the moments , are often referred to by corresponding names such as the conditional mean and conditional variance .
In the latter two examples the law of total probability is irrelevant, since only a single event (the condition) is given. By contrast, in the example above the law of total probability applies , since the event X = 0.5 is included into a family of events X = x where x runs over (−1,1), and these events are a partition of the probability space.
denotes the corresponding decision problem. Note that c R is a search problem while #R is a decision problem, however c R can be C Cook-reduced to #R (for appropriate C) using a binary search (the reason #R is defined the way it is, rather than being the graph of c R, is to make this binary search possible).