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{"ops":[{"insert":" 1. (i) Interpret the coefficients in the final two columns of the following table. Explain (briefly) why the results here suggested there was an inefficiency. (ii) A tennis player\u2019s serve lands in with probability x. Conditional on the serve being in, the server wins the point with probability 0.9025 \u2212 \ufffd2 3 . Find the optimal value for the second serve, x2. Show that the optimal value for the first serve, x1, is smaller than x2. Explain why this occurs. (iii) Juan has a batting average of .350 with runners in scoring position (i.e., a teammate is on second and\/or third base). He has a batting average of .300 when there are no runners in scoring position. Fernando has a batting average of .340 with runners in scoring position and .290 with no runners in scoring position. What can we conclude about Juan\u2019s overall batting average relative to Fernando\u2019s? (iv) Explain what Abramitzky et al. found concerning success rates for line call challenges.\u00a0\n"}]}

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