How that x and y are independent normal random variable

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Suppose that R and U are independent continuous random variables where U has a Uniform distribution on [0, 1] and R has the density function

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(a) Show that R2 has an Exponential distribution.

(b) Define X = R cos(2πU) and Y = R sin(2πU). Show that X and Y are independent standard Normal random variables.

(c) Suggest a method for generating Normal random variables based on the results in part (a) and (b).

Reference no: EM131212159

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