Let U1,U2U_1, U_2U1,U2 be independent Uniform(0,1)\text{Uniform}(0, 1)Uniform(0,1) variables. 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?
Standard Normal N(0,1)N(0, 1)N(0,1)
Exponential(1)
Cauchy(0, 1)
Uniform(0, 1)