Answered: X = √-2 log U cos(2πV), Find the joint… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.3: The Addition And Subtraction Formulas

Problem 76E

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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).

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