Considering the antithetic variates method [see (6.3.7a,b)], explain why Note that the amount of computational work to

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Considering the antithetic variates method [see (6.3.7a,b)], explain why 

var (+) - (var() = 2 [var(ci) + cov(ci, i)].

Note that the amount of computational work to generate c̄AV [see (6.3.8)] is about twice the work to generate ĉ. By applying (6.3.5), show that the antithetic variates method improves computational efficiency provided that

cov (ci, i)  0.

Give a statistical justification why the above negative correlation property is in general valid (Boyle, Broadie and Glasserman, 1997).

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