In Sec. 11.3 we discussed the conditions under which AV would work or backfire. Consider t...

In Sec. 11.3 we discussed the conditions under which AV would work or backfire. Consider the following simple Monte Carlo examples, where U represents a random number:

(1) X_j = U²

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(2) X_j = 4(U – 0.5)²

(a) Sketch the graph of the response in both examples.

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(b) For each example, analytically find .

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(c) For each example, analytically calculate  under both independent sampling and AV.

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(d) Confirm your calculations in (b) and (c) empirically by designing and carrying out a small simulation study.