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Probability density function (view source)
Revision as of 03:19, December 13, 2007
, 03:19, December 13, 2007New page: In probability theory, a ''probability density function'' (say) ''f'' is a real valued and continuous function whose value is the probability density of the variable that it is a funct...
In [[probability theory]], a ''probability density function'' (say) ''f'' is a real valued and continuous function whose value is the probability density of the variable that it is a function of. Since it is a density, the actual probability P that the variable will be in the interval [a,b] is
:<math>P(a \leq x \leq b) = \int_a^b f(x) \, dx </math>
This density function is intended to express mathematically the total apportionment of the values of the variable it represents over its entire [[domain]]. In order to qualify, such a function must meet the following criteria:
(1) <math> \int_{-\infty}^\infty \,f(x)\,dx = 1. </math> i.e., finitely convergent (to unity by convention).
(2) <math> \int_{-\infty}^a \,f(x)\,dx \leq \int_{-\infty}^b \,f(x)\,dx </math> for a<b, i.e., is non-decreasing
[[Category:mathematics]]
:<math>P(a \leq x \leq b) = \int_a^b f(x) \, dx </math>
This density function is intended to express mathematically the total apportionment of the values of the variable it represents over its entire [[domain]]. In order to qualify, such a function must meet the following criteria:
(1) <math> \int_{-\infty}^\infty \,f(x)\,dx = 1. </math> i.e., finitely convergent (to unity by convention).
(2) <math> \int_{-\infty}^a \,f(x)\,dx \leq \int_{-\infty}^b \,f(x)\,dx </math> for a<b, i.e., is non-decreasing
[[Category:mathematics]]