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Thus, by assuring , the probability of making one or more type I errors in the family is controlled at level . A procedure controls the FWER in the weak sense if the FWER control at level α {\displaystyle \alpha \,\!} is guaranteed only when all null hypotheses are true (i.e. when m 0 = m {\displaystyle m_{0}=m} , meaning the "global null ...
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Probability theory is applied in everyday life in risk assessment and modeling. The insurance industry and markets use actuarial science to determine pricing and make trading decisions. Governments apply probabilistic methods in environmental regulation, entitlement analysis, and financial regulation.
The probability is sometimes written to distinguish it from other functions and measure P to avoid having to define "P is a probability" and () is short for ({: ()}), where is the event space, is a random variable that is a function of (i.e., it depends upon ), and is some outcome of interest within the domain specified by (say, a particular ...
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.
Distributional assumptions. Where a statistical model involves terms relating to random errors, assumptions may be made about the probability distribution of these errors. [5] In some cases, the distributional assumption relates to the observations themselves. Structural assumptions.
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 .
The conditional probability based on the intersection of events defined as: = (). [2] satisfies the probability measure requirements so long as () is not zero. [ 3 ] Probability measures are distinct from the more general notion of fuzzy measures in which there is no requirement that the fuzzy values sum up to 1 , {\displaystyle 1,} and the ...
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