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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 14EQ

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Question

Let (X₁, X₂) be a pair of standard exponential random variables with the countermonotonicity
copula and let U be a standard uniform random variable.
a) Find a stochastic representation of the form (X₁, X₂) = (f(U), g(U)) for functions f and g
which shows how (X₁, X2) can be simulated.
b) With the help of a), use software and numerical integration to calculate the minimal
correlation for two standard exponential random variables.

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