Soccer Strategy In soccer, serious fouls in the penalty box result in a penalty kick with one kicker and one defending goalkeeper. The table below summarizes results from 286 kicks during games among top teams (based on data from “Action Bias Among Elite Soccer Goalkeepers: The Case of Penalty Kicks.” by Bar-Eli et al., Journal of Economic Psychology. Vol. 28, No. 5). In the table, jump direction indicates which way the goalkeeper jumped, where the kick direction is from the perspective of the goalkeeper. Use a 0.05 significance level to test the claim that the direction of the kick is independent of the direction of the goalkeeper jump. Do the results support the theory that because the kicks are so fast, goalkeepers have no time to react, so the directions of their jumps are independent of the directions of the kicks?
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- 2. Which of the following statements are (not) true? lim sup{An U Bn} 818 lim sup{A, B} 818 lim inf{An U Bn} 818 818 lim inf{A, B} An An A, Bn- A, BnB →B = = = lim sup A, U lim sup Bn; 818 818 lim sup A, lim sup Bn; 818 81U lim inf A, U lim inf Bn; 818 818 lim inf A, lim inf Bn; n→X 818 An U BRAUB as no; An OBRANB as n→∞.arrow_forwardThroughout, A, B, (An, n≥ 1), and (Bn, n≥ 1) are subsets of 2. 1. Show that AAB (ANB) U (BA) = (AUB) (AB), Α' Δ Β = Α Δ Β, {A₁ U A2} A {B₁ U B2) C (A1 A B₁}U{A2 A B2).arrow_forward16. Show that, if X and Y are independent random variables, such that E|X|< ∞, and B is an arbitrary Borel set, then EXI{Y B} = EX P(YE B).arrow_forward
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