hw6 - AMS 553: Homework 6 1. (L&K 11.2) In...

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Unformatted text preview: AMS 553: Homework 6 1. (L&K 11.2) In Section 11.2.2 and specifically in figure 11.1, We consider the question of whether CRN would induce the desired positive correlation for a given pair of alternative configurations, or whether it might backfire. Consider the following simple Monte Carlo examples, where U represents a random number: (a) X 1 j = U 2 and X 2 j = U 3 (b) X 1 j = U 2 and X 2 j = (1- U ) 3 (a) Sketch the graphs of the responses in both examples. (b) For each example, analytically find Cov ( X 1 j ,X 2 j ). (c) For each example, analytically calculate V ar ( X 1 j- X 2 j ) under both independent sampling and CRN. (d) Confirm your calculations in (b) and (c) empirically by designing and carrying out a small simu- lation study. 2. (L&K 11.3) In Section 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: (a) X j = U 2 (b) X j = 4( U- . 5) 2 (a) Sketch the graphs of the responses in both examples.(a) Sketch the graphs of the responses in both examples....
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