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fall 2005 STAT 230 test4soln

fall 2005 STAT 230 test4soln - STAT 230 Test#4 November 8...

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STAT 230 Test #4 November 8, 2005 4:30 – 5:15 pm 1. Two numbers U and V are randomly selected from 1, 2 and 3 with replacement . Let X = min { U, V } and Y = max { U, V } . [4] (a) Find the two missing values of the joint probability function of ( X, Y ) in the following table: x f ( x, y ) 1 2 3 1 1/9 0 0 y 2 2/9 (1/9) 0 3 2/9 (2/9) 1/9 [5] (b) Find the marginal probability function of Y . y 1 2 3 f Y ( y ) 1 / 9 1 / 3 5 / 9 [5] (c) Find the conditional probability P ( Y = 2 | X = 1). P ( Y = 2 | X = 1) = f (1 , 2) f X (1) = 2 / 9 5 / 9 = 2 5 . [3] (d) Are X and Y independent? Why or why not? X and Y are not independent, since f X (1) × f Y (1) = (5 / 9) × (1 / 9) 6 = f (1 , 1). ( Note : this inequality can be replaced by other similar ones; Another acceptable answer is “ X and Y are not independent, since X Y ”) 2. In a public opinion survey over a large population, each respondent chooses one and only one answer from five possible answers: A. Strongly Agree; B. Agree; C. Disagree; D. Strongly Disagree; E. Don’t Know. For a randomly selected individual, the probabilities that he/she chooses one of the five answers are listed in the following table.
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