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Question 1: A researcher is interested in the relationship between being a smoker and eating sugar among undergraduate students

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Question 1: A researcher is interested in the relationship between being a smoker and eating sugar among undergraduate students. The researcher interviews a random sample of n students. Let X: be a random variable that indicates whether the im person in the sample is a smoker: 0 = No, 1 = Yes. The researcher ?nds that a proportion p of the undergraduate students are smokers. Let Yi be a random variable that indicates whether the im person in the sample claims to eat sugar: 0 = No, 1 = Yes. Conditional on being a smoker, person i will claim not to eat sugar with probability :2; when interviewed. Conditional on being a non-smoker, person i always claims not to eat sugar when interviewed. a. Write the joint distribution of Xiand Yl in tabular form, arranging X1 in the rows and Y: in the columns of your table. Your answer should be expressed in terms of p and q. b. Using your answer to the preceding question, calculate the marginal probability for Yi. c. Using your answers to the preceding questions, calculate E()() and E(Y).