joint continuous density function

Let X1,X2,,Xn be n random variablesMathworldPlanetmath all defined on the same probability spaceMathworldPlanetmath. The joint continuous density function of X1,X2,,Xn, denoted by fX1,X2,,Xn(x1,x2,,xn), is the function fX1,X2,,Xn:n such that for any domain Dn, we have


As in the case where n=1, this function satisfies:

  1. 1.

    fX1,X2,,Xn(x1,,xn)0 (x1,,xn)

  2. 2.


As in the single variable case, fX1,X2,,Xn does not represent the probability that each of the random variables takes on each of the values.

Title joint continuous density function
Canonical name JointContinuousDensityFunction
Date of creation 2013-03-22 11:54:58
Last modified on 2013-03-22 11:54:58
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 11
Author mathcam (2727)
Entry type Definition
Classification msc 60A10
Synonym joint mass function
Synonym joint density function
Synonym joint distribution