Distribution of the Sum of Two Independent Uniform Random Variables on the Unit Interval (0,1)

Assuming U1 and U2 are independent uniform random variables on the interval (0,1), the distribution of the sum S = U1 + U2 is symmetric triangular (the PDF has a symmetric triangular shape with a mean of 1). https://amzn.to/3rjDOoA (Probability and Statistics with Applications: A Problem Solving Text, by Asimow and Maxwell)

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