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Difficulty: Hard
Category: Probability & Statistics
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Topics: probability, jacobian, transformation, normal-distribution
Let $X$ and $Y$ be independent and identically distributed (i.i.d.) standard normal random variables. Define new random variables $R$ and $\Theta$ such that $X = R \cos{\Theta}$ and $Y = R \sin{\Theta}$. Find the joint probability density function (PDF) $f(r, \theta)$ of $R$ and $\Theta$.
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