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Distributionshard
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Consider two independent random variables U1,U2∼Uniform(0,1)U_1, U_2 \sim \text{Uniform}(0, 1)U1​,U2​∼Uniform(0,1). Define Z=−2ln⁡(U1)cos⁡(2πU2)Z = \sqrt{-2 \ln(U_1)} \cos(2\pi U_2)Z=−2ln(U1​)​cos(2πU2​). What is the distribution of ZZZ?