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The '''probability density function''' of a continuous [[random variable]] is the function that provides the likelihood that the variable will have a value in a given interval when the function is integrated over that same interval.  Stated another way, a ''probability density function'' ''f'' is a non-negative valued real 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

The '''probability density function''' of a continuous [[random variable]] is the function that provides the likelihood that the variable will have a value in a given interval when the function is integrated over that same interval.  Stated another way, a '''probability density function''' ''f'' is a non-negative valued real 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>

:<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 the variables entire [[domain]].  This "apportionment" can signify different things in various contexts, such as relative proportion of observations, or [[information]] regarding the residual uncertainty of its true value.  

This density function is intended to express mathematically the total apportionment of the values of the variable it represents over the variables entire [[domain]].  This "apportionment" can signify different things in various contexts, such as relative proportion of observations, or [[information]] regarding the residual uncertainty of its true value.  

[[Category:mathematics]]

[[Category:mathematics]]

[[Category:probability]]

[[Category:probability]]

[[Category:probability and statistics]]

[[Category:Probability and Statistics]]