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Probability theory is the formalization and study of the mathematics of uncertain events or knowledge. The related field of mathematical statistics develops statistical theory with mathematics. Statistics , the science concerned with collecting and analyzing data, is an autonomous discipline (and not a subdiscipline of applied mathematics ).
The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]
A discrete probability distribution is the probability distribution of a random variable that can take on only a countable number of values [15] (almost surely) [16] which means that the probability of any event can be expressed as a (finite or countably infinite) sum: = (=), where is a countable set with () =.
This is the same as saying that the probability of event {1,2,3,4,6} is 5/6. This event encompasses the possibility of any number except five being rolled. The mutually exclusive event {5} has a probability of 1/6, and the event {1,2,3,4,5,6} has a probability of 1, that is, absolute certainty.
Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to ...
Biology uses probability extensively in fields such as ecology or neurobiology. [140] Most discussion of probability centers on the concept of evolutionary fitness . [ 140 ] Ecology heavily uses modeling to simulate population dynamics , [ 140 ] [ 141 ] study ecosystems such as the predator-prey model, measure pollution diffusion, [ 142 ] or to ...
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