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Mid2Problems2A - Midterm Exam 2 Practice Problems Answer...

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Unformatted text preview: Midterm Exam 2 Practice Problems - Answer Key 1. A fictional study examined the joint probability distribution of political affiliation and car purchasing patterns. Political affiliation is in the left most column, and car preference on the top most row. Party/Car Hummer Honda Accord Toyota Prius Republican 0.15 0.25 0.1 Democrat 0.3 0.2 (a) What the probability of someone buying a Hummer? What is the probability of buying an Accord? What is the probability of purchasing a Prius? Let C denote car and P denote party. We find P ( C = Hummer ) by noting P ( C = Hummer ) = P ( C = Hummer,P = R ) + P ( C = Hummer,P = D ) = 0 . 15 + 0 = 0 . 15 Similarly we get P ( C = Accord ) = 0 . 55 and P ( C = Prius ) = 0 . 3. (b) What is the probability of purchasing a Prius conditional on being a democrat? What is the probability of purchasing a Prius conditional on being a Republican? Recall that the conditional probability is given by P ( C = Prius | P = D ) = P ( C = Prius,P = D ) /P ( P = D ) = 0 . 2 / . 5 = 2 / 5 Similarly, we obtain P ( X = Prius | P = R ) = 1 / 5. (c) Are party affiliation and car purchasing patterns independent of each other? Justify your answer. They are not. There are different ways to see this. The easiest one is to note that under independence P ( C = Prius | P = D ) = P ( C = Prius | P = R ), but this is not true from (b)....
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Mid2Problems2A - Midterm Exam 2 Practice Problems Answer...

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