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| = Probability Notation = Statisticians love technical language. When keywords and specific names become too verbose, they invent a notation. See also some [[Statistics/SigmaAlgebraNotation|σ algebra notation]], [[Statistics/BayesianNotation|Bayesian notation]], [[Statistics/JointProbability|joint probability notation]], [[Statistics/ConditionalProbability|conditional probability notation]], [[Statistics/ExpectedValues|expected value notation]], and [[Statistics/ConditionalExpectations|conditional expectation notation]]. <<TableOfContents>> ---- == Distribution == A random variable is distributed by some function. This relationship is notated with a tidle, as in ''X ~ Bernoulli''. ---- == Expected Values == The expected value of ''X'' is notated as ''E[X]''. ---- == Probability mass functions == A discrete random variable is distributed by a '''probability mass function''' ('''PMF'''). This is typically notated as ''p(X=x)''. Sometimes the function is named ''P'' (capitalized) or ''Pr'' instead. For [[Statistics/BernoulliDistribution|Bernoulli-distributed]] random variables, because the only possible values are 0 and 1, and because the 0 term evaluated out of most equations, a shorthand notation is commonly used. ''p(X=1) = p(X)''. Sometimes a probability function is notated with a subscript to emphasize what random variable it described. For example, ''p,,X,,(x) = p(X=x)''. ---- == Probability density functions == A continuous random variable is distributed by a '''probability density function''' ('''PDF'''). While such a function may be expressed as ''p(X=x)'' (or ''p,,X,,(x)''), it isn't possible to evaluate this function at a single value. See CDFs instead. ---- == Cumulative distribution functions == The probability that a random variable takes a value equal or less than ''x'' is given by a '''cumulative distribution function''' ('''CDF'''). For discrete variables, this is a summation of the PMF for all values from 0 to ''x''. For continuous variables, this is the integral of the PDF from 0 to ''x''. If a CDF is named ''F'' then it is evaluated like ''F,,X,,(x) = P(X <= x)''. ---- CategoryRicottone |
