How Do You Calculate Marginal Density for fX(x) Given fX,Y(x,y)?

[qwertydh]

Homework Statement

Calculate the marginal density of fx (x).
Fx,y (x,y) = double integral of 4x.e^(x+y) when 0<x<y, 0 otherwise.

Homework Equations

The Attempt at a Solution

i set up the equation as fx (x) = integral from x up to infinity of 4x.e^(x+y) dy

i get 4x [e^(x+y)] from x to infinity,

thats when the problem arises as whatever i do there's always infinity in the question.

I'm told the answer is 4x.e^(-2x)

any help would be really appreciated.
thanks.

 

[lanedance]

are you sure you haven't missed a minus sign in the original distribution>
$$f_{X,Y} (x,y)dxdy = 4xe^{-(x+y)}dx dy$$

would make more sense, the distrubution you gave is unbounded