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Standard deviation can also be used to calculate standard ... Particle physics conventionally uses a standard of "5 sigma" for the declaration of a discovery. A five ...
The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed , and is called a normal deviate . Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not ...
In the empirical sciences, the so-called three-sigma rule of thumb (or 3 σ rule) expresses a conventional heuristic that nearly all values are taken to lie within three standard deviations of the mean, and thus it is empirically useful to treat 99.7% probability as near certainty.
The table shown on the right can be used in a two-sample t-test to estimate the sample sizes of an experimental group and a control group that are of equal size, that is, the total number of individuals in the trial is twice that of the number given, and the desired significance level is 0.05. [4]
The characteristic function + = ((+)) of the sum of two independent random variables X and Y is just the product of the two separate characteristic functions: = (), = ()
when the probability distribution of the value is known, it can be used to calculate an exact confidence interval; when the probability distribution is unknown, Chebyshev 's or the Vysochanskiï–Petunin inequalities can be used to calculate a conservative confidence interval; and
In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field, where the σ comes from the German "Summe" [1]) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections. The ordered pair (,) is called a measurable space.
If the considered function is the density of a normal distribution of the form = [()] where σ is the standard deviation and x 0 is the expected value, then the relationship between FWHM and the standard deviation is [1] = .