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The law of total probability is [1] a theorem that states, in its discrete case, if is a finite or countably infinite set of mutually exclusive and collectively exhaustive events, then for any event. or, alternatively, [1] where, for any , if , then these terms are simply omitted from the summation since is finite.
Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting conditional probabilities, allowing us to find the probability of a cause given its effect. [1] For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual ...
v. t. e. Probability is a measure of the likeliness that an event will occur. Probability is used to quantify an attitude of mind towards some proposition whose truth is not certain. The proposition of interest is usually of the form "A specific event will occur." The attitude of mind is of the form "How certain is it that the event will occur?"
The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. [1] These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. [2] There are several other (equivalent) approaches to formalising ...
In probability theory, the central limit theorem (CLT) states that, in many situations, when independent and identically distributed random variables are added, their properly normalized sum tends toward a normal distribution. This article gives two illustrations of this theorem. Both involve the sum of independent and identically-distributed ...
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a ...
Characterization of probability distributions. Chung–Erdős inequality. Condorcet's jury theorem. Continuous mapping theorem. Contraction principle (large deviations theory) Coupon collector's problem. Cox's theorem. Cramér–Wold theorem. Cramér's theorem (large deviations)
In probability theory, the law of large numbers (LLN) is a mathematical law that states that the average of the results obtained from a large number of independent random samples converges to the true value, if it exists. [1] More formally, the LLN states that given a sample of independent and identically distributed values, the sample mean ...
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