# Distribution function of 2D random vector

1. Mar 2, 2010

### liorda

1. The problem statement, all variables and given/known data
Write the distribution function of the 2D random vector which is uniformly distributed in the triangle with the corners {(0,0),(0,1),(1,0)}.

2. Relevant equations
$$F_{X,Y} (x,y) = Pr(X \le x, Y \le y)$$

3. The attempt at a solution
Sorry, but I don't know even where to start. I guess the vector is (X,Y), where X and Y are the coordinates of the "head" of the vector. The vector is uniformly distributed among the triangle area, but X and Y are not uniformly distributed between [0,1]. I don't know how to express the relation between them nor how to continue.

Solution
http://img696.imageshack.us/img696/663/screenshotow.png [Broken]

Last edited by a moderator: May 4, 2017