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.
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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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