Question: BoxMuller method for sampling from normal distributions, 1958. Let U; V be independent random variables with uniform distribution on 0; 1OE , and define R

Box–Muller method for sampling from normal distributions, 1958. Let U; V be independent random variables with uniform distribution on 0; 1OE , and define R D p

2 logU, X D R cos.2V /, and Y D R sin.2V /. Show that X; Y are independent and N0;1-

distributed. Hint: First calculate the distribution density of R and then use the polar coordinate transformation of double integrals.

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