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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)

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)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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).
Transcribed Image Text: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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