PDF of the sum of three continous uniform random variables

  • Thread starter peteron
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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=[tex]\int[/tex][tex]\int[/tex]f_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.
 
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Answers and Replies

  • #2
lanedance
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start with an easier problem first
Y = X1 & X2

it you're still getting no where, try looking up convolutions
 
  • #3
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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...
 
  • #4
lanedance
Homework Helper
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so if you can find the pdf of Y = X1 + X2, then consider Z = Y + X3
 

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