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Confusing in transforming variable

  1. May 5, 2012 #1
    Considering U1 and U2 which both follow Uniform (0 , A), then after
    the transformation of variable, i can find x=(U1+U2)/2 has f(x)=2/A(both
    my classmates and me get this result). However i am confused that when i
    integrate x by it range from 0 to A (because U1 and U2 both ranged from
    0 to A), the prob equals 2 instead of 1. What's wrong with my mind?
    steps : http://desmond.imageshack.us/Himg848/scaled.php?server=848&filename=steps.png&res=landing [Broken]
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. May 6, 2012 #2


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    Science Advisor

    I can't follow your derivation, but the answer is completely wrong.
    Let U=(U1+U2)/2. The density function for U is not uniform.
    It looks like two sides of an isosocles triangle with the base from 0 to A on the x axis and the peak of the triangle is at x = A/2. The two sides have equations: y=(4/A2)x and y = (4/A2)(A - x).
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