Changes

(1) <math> \int_{-\infty}^\infty \,f(x)\,dx = 1. </math>  i.e., finitely convergent (to unity by convention).

(1) <math> f(x) \geq 0 </math>  <math> \forall x </math>  inside the domain of support.

(2) <math> \int_{-\infty}^a \,f(x)\,dx \leq \int_{-\infty}^b \,f(x)\,dx </math>  for a<b,  i.e., is non-decreasing

 

(2) <math> \int_{-\infty}^\infty \,f(x)\,dx = 1. </math>  i.e., finitely convergent (to unity by convention).

 

 

(3) <math> \int_{-\infty}^a \,f(x)\,dx \leq \int_{-\infty}^b \,f(x)\,dx </math>  for a<b,  i.e., is non-decreasing

Such a function leads to the definition of an associated [[cumulative distribution function]].

Such a function leads to the definition of an associated [[cumulative distribution function]].

If the [[domain]] of the variable is [[finite]], then the infinite limits on the above integrals would be replaced by those bounds, and a third requirement would be:

If the [[domain]] of the variable is [[finite]], then the infinite limits on the above integrals would be replaced by those bounds, and a fourth requirement would be:

(3) <math> f(x) = 0 </math>  <math> \forall x </math>  outside the finite domain of support.

(4) <math> f(x) = 0 </math>  <math> \forall x </math>  outside the finite domain of support.

[[Category:mathematics]]

[[Category:mathematics]]