SSuppose that you choose a point at random in the tetrahedron formed by the planes x=0, y=0, z=0, and x+y+z=1. Let X,Y,Z represent the x-, y-, and z-coordinates of that point, respectively.
(a) Find the joint probability density function of X, Y and Z.
(b) Find the probability density function of Z marginalized over X and Y.

Question

SSuppose that you choose a point at random in the tetrahedron formed by the planes x=0, y=0, z=0, and x+y+z=1. Let X,Y,Z represent the x-, y-, and z-coordinates of that point, respectively. 
(a) Find the joint probability density function of X, Y and Z. 
(b) Find the probability density function of Z marginalized over X and Y.

Quizplus · Accepted Answer

The Answer of SSuppose that you choose a point at random in the tetrahedron formed by the planes x=0, y=0, z=0, and x+y+z=1. Let X,Y,Z represent the x-, y-, and z-coordinates of that point, respectively. 
(a) Find the joint probability density function of X, Y and Z. 
(b) Find the probability density function of Z marginalized over X and Y.

SSuppose That You Choose a Point at Random in the Tetrahedron