In comparing two system configurations, consider using AV and CRN together, i.e., use AV w...

In comparing two system configurations, consider using AV and CRN together, i.e., use AV within a pair of runs of each configuration, and CRN across the configurations. To simplify things, suppose we make just one pair of runs of each configuration, shown schematically below:

The estimator of .

(a) Find an expression for Var(Z) in terms of the variances and covariances corresponding to the four runs in the above schematic.

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(b) Assume that both CRN and AV work on their own, i.e., induce correlations of the desired signs. Does the combined scheme then work? That is, do we know that this scheme will reduce Var(Z) in comparison to independent sampling throughout? Explain.