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Unformatted text preview: EC2019 SAMPLING AND INFERENCE, 2010 QUESTIONS IN PREPRATION FOR THE EXAMINATION The examination asks for THREE answers The time allowed is TWO hours 1. Give an account of the axioms of Boolean algebra and, in the process, compare them with the axioms of arithmetic. Let A and B be two events within the sample space S , for which P ( S ) = 1. Let A c and B c be the complements of A and B respectively. Given that P ( A B c ) = 0 . 3 and P ( A B ) = 0 . 1, find P ( B ). 2. Show how Bayes theorem is used to obtain the posterior likelihood of an hypothesis from the prior likelihood when an event has occured which throws some light on the hypothesis. Usually I wash the breakfast dishes before leaving for the oce. If I do not do so, then my wife will do so nine times out of ten if she returns from work first; but there is only a one-in-ten chance that my children will do so if they return from school before I get home....
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- Spring '12