Multivariate Density Function
A non-negative function on whose iterated integrals give .
Definition 4.21 (Multivariate Density Function)
Let be a random vector. We say that has a multivariate density function if there exists a non-negative function such that for all ,
The probability distribution function of is defined as
Recovering the density and integrating over sets
When has multivariate density and distribution function ,
and probabilities of general regions are obtained by integration:
Related
Stated in
- Definition 4.21 (Multivariate Density Function)§4.6.1 Introduction