Let X have a standard Cauchy distribution. Assuming you have U Uniform(0; 1), explain how to

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Let X have a standard Cauchy distribution.1 Fx(x)==arctan(r) + 1 2

Assuming you have U ∼ Uniform(0; 1), explain how to generate X. Then, use this result to produce 1000 samples of X and compute the sample mean. Repeat the experiment 100 times. What do you observe and why?

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