Fractional part of sum of two uniforms Can we prove that {U1+U2} (fractional part of sum of two uniforms(0,1) ) is also uniformly distributed in [0,1]?

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.
