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Random Variableshard
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Consider a random variable XXX with PDF f(x)=1π(1+x2)f(x) = \frac{1}{\pi(1+x^2)}f(x)=π(1+x2)1​. If we define Y=arctan⁡(X)Y = \arctan(X)Y=arctan(X), what is the range and density of YYY?