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Help on the density of sum of two uniform variables.

  1. Jun 17, 2005 #1
    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:
     
  2. jcsd
  3. Jun 17, 2005 #2

    mathman

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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).
     
  4. Jun 18, 2005 #3
    yep, you are right. thanks!
     
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