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Medium · Probability & Statistics · Quant Trader interview question · probability, random-variable, transformation, pdf, uniform-distribution
Suppose $X$ is a random variable that follows a standard uniform distribution on the interval (0, 1), denoted as $X \sim \text{Uniform}(0, 1)$. Define a new random variable $Y$ as $Y = X^2$. What is the probability density function (PDF) of $Y$, denoted as $f_Y(y)$?