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The Convolution Challenge

Medium · Probability & Statistics · Quant Trader interview question · probability, distribution, convolution, uniform, integration

Let $X$ and $Y$ be independent random variables, each uniformly distributed on the interval $0, 1$. That is, $X, Y \sim \text{Uniform}(0, 1)$. Determine the probability density function (PDF) of the random variable $Z = X + Y$.