# PDF of the sum of three continous uniform random variables

## Homework Statement

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

## The Attempt at a Solution

PDF of Z, f_z=$$\int$$$$\int$$f_x1(z-x2-x3)*f_x2*f_x3 dx2 dx3

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lanedance
Homework Helper
Y = X1 & X2

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

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