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3. [113 + l pts total] Suppose that the random variable Y is uniformly distributed on the interval {af, am}. Find the probability density function (13de- of U = tanY using rst the Method of Distribution Functions and then the Method of Transformations, verifying all required assumptions. Note: the distribution of U is called the Cauchy distribution. It is often used in models of volatile data, such as stock returns due to its heavy tails. One interesting feature of this distribution is that its mean (and all higher moments} are not defined. [Hints: l - Recall the shape and properties of the tan(} function and its inverse from your math classes; try sketching the transformation function and its inverse to get a better idea of what it looks like u the derivative of the inverse tangent function is % tan1(1) = g - the derivative of the tangent function is 3: tan{:r} 2 see2 [I]