Probability And Statistics
Probability and statistics are two closely related fields in mathematics, sometimes combined for academic purposes. They are covered in several articles: * Probability * Statistics * Glossary of probability and statistics * Notation in probability and statistics * Timeline of probability and statistics The following is a timeline of probability and statistics. Before 1600 *8th century – Al-Khalil, an Arab mathematician studying cryptology, wrote the ''Book of Cryptographic Messages''. The work has been lost, but based on the reports of ...

Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written ...
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Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ...
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Glossary Of Probability And Statistics
This glossary of statistics and probability is a list of definitions of terms and concepts used in the mathematical sciences of statistics and probability, their sub-disciplines, and related fields. For additional related terms, see Glossary of mathematics and Glossary of experimental design. A B C D E F G H I J K L M N O P Q R S T ...
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Notation In Probability And Statistics
Probability theory and statistics have some commonly used conventions, in addition to standard mathematical notation and mathematical symbols. Probability theory * Random variables are usually written in upper case roman letters: ''X'', ''Y'', etc. * Particular realizations of a random variable are written in corresponding lower case letters. For example, ''x''1, ''x''2, …, ''x''''n'' could be a sample corresponding to the random variable ''X''. A cumulative probability is formally written P(X\le x) to differentiate the random variable from its realization. * The probability is sometimes written \mathbb to distinguish it from other functions and measure ''P'' so as to avoid having to define "''P'' is a probability" and \mathbb(X\in A) is short for P(\), where \Omega is the event space and X(\omega) is a random variable. \Pr(A) notation is used alternatively. *\mathbb(A \cap B) or \mathbb \cap A/math> indicates the probability that events ''A'' and ''B'' both occur. The join ...
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