X = √-2 log U cos(2πV), Find the joint distribution of X and Y. (Hint: you may want to first compute the distribution of √-2 log U). Y:= √-2 log U sin(27V)
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![4. (Box-Muller transform) Let U and V be independent random variables that
are uniformly distributed on [0, 1]. Define
X = √-2 log U cos(2πV), Y = √-2 log U sin(27V)
Find the joint distribution of X and Y.
(Hint: you may want to first compute the distribution of √-2 log U).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97e612ef-1556-436b-b62c-352b280e9e69%2F3ebd7639-5334-4fa1-be39-60cc4270f9c4%2Fg116mia_processed.png&w=3840&q=75)
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