Help on the density of sum of two uniform variables.

  • Thread starter gimmytang
  • Start date
Hi, I need to calculate the density function of Z=X+Y, where X and Y are independent uniform distributed on [0,1]. The calculation is in the following:
[tex]f_{Z}(z)=\int_{A}dx[/tex]
a. If 0<z<1, A={x:0<x<z} then f(z) = z;
b. If 1<z<2, A={x:0<x<1} then f(z) = 1;
Step b is wrong, but I don't know where I am wrong. Any hint will be appreciated!
Thanks
gim :cry:
 

mathman

Science Advisor
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For step b, the domain of x is z-1 to 1, so f(z)=2-z.

The reason for that is z-x=y, which is restricted to (0,1).
 
yep, you are right. thanks!
 

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