if and are positively correlatedthe variance of - would be smaller than if and are independent show that this is not always the case by providing counter-example (ccontinuing ( )assume now that and are continuous show that the variance of by taking common random numbers is no larger than when and are independent [hintuse the following lemma of hoeffding [ ]if (xyhave joint cdf with marginal cdfs of and being and grespectivelythen ( (xyf(xg( )dx dycov(xyprovided cov(xyexists