PDF of the sum of three continous uniform random variables

[peteron]

Homework Statement

X1, X2, X3 are three random variable with uniform distribution at [0 1]. Solve the PDF of Z=X1+X2+X3.

Homework Equations

The Attempt at a Solution

PDF of Z, f_z=\int\intf_x1(z-x2-x3)*f_x2*f_x3 dx2 dx3

I saw the answer at http://eom.springer.de/U/u095240.htm, but I cannot figure out how to get there...please help.

 

[lanedance]

start with an easier problem first
Y = X1 & X2

it you're still getting no where, try looking up convolutions

 

[peteron]

start with an easier problem first
Y = X1 & X2

it you're still getting no where, try looking up convolutions

I know how to solve the case of two variables, but got stunned in the case of three variables...

 

[lanedance]

so if you can find the pdf of Y = X1 + X2, then consider Z = Y + X3