Concept explainers
(Exercises 19–26) For each description of data, identify Who and What were investigated and the Population of interest.
23. Honesty Coffee stations in offices often just ask users to leave money in a tray to pay for their coffee, but many people cheat. Researchers at Newcastle University alternately taped two posters over the coffee station. During one week, it was a picture of flowers; during the other, it was a pair of staring eyes. They found that the average contribution was significantly higher when the eyes poster was up than when the flowers were there. Apparently, the mere feeling of being watched—even by eyes that were not real—was enough to encourage people to behave more honestly. (Source: NY Times, Dec. 10, 2006)
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- 6. Show that 1{AU B} = max{1{A}, I{B}} = I{A} + I{B} - I{A} I{B}; I{AB} = min{I{A}, I{B}} = I{A} I{B}; I{A A B} = I{A} + I{B}-21{A} I {B} = (I{A} - I{B})².arrow_forwardTheorem 3.5 Suppose that P and Q are probability measures defined on the same probability space (2, F), and that F is generated by a л-system A. If P(A) = Q(A) for all A = A, then P = Q, i.e., P(A) = Q(A) for all A = F.arrow_forward6. Show that, for any random variable, X, and a > 0, Lo P(x -00 P(x < xarrow_forward5. Suppose that X is an integer valued random variable, and let mЄ N. Show that 8 11118 P(narrow_forward食食假 6. Show that I(AUB) = max{1{A}, I{B}} = I{A} + I{B} - I{A} I{B}; I(AB)= min{I{A}, I{B}} = I{A} I{B}; I{A A B} = I{A} + I{B}-21{A} I{B} = (I{A} - I{B})². -arrow_forward11. Suppose that the events (An, n ≥ 1) are independent. Show that the inclusion- exclusion formula reduces to P(UAL)-1-(1-P(Ak)). k=1 k=1arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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