Can we prove that {U1+U2} (fractional part of sum of two uniforms(0,1) ) is also uniformly distributed in [0,1]?
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Please tell us what you have tried and where you are having trouble. – BruceET Oct 20 '15 at 02:28
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Yes. Find the PDF of the sum, which is a triangular distribution on $(0,2)$, and then the PDF of the fractional part is the value at $a$ added to the value at $1+a$ for $0<a<1$. Maybe there's a way without appealing to the PDFs, but this will work.
Chappers
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Well, observe that the distribution of the sum's fractional part, conditioned on any given value of $U_1$, is also uniform. If all the conditional distributions are uniform, the unconditional distribution must also be uniform.
Brian Tung
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