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Let U1, U2 be two independent uniform random variables on (0, 1). Let 0 = 2xU, and S = - log U2 (natural log). Show

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Let U1, U2 be two independent uniform random variables on (0, 1). Let 0 = 2xU, and S = - log U2 (natural log). Show that S has an exponential distribution, X = v2.S cos(0) and Y = v2. sin(0) are independent normal random variables. This gives a method for simulating normal random variables using only uniform (0, 1) random variables and elementary functions

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