AK3_230

# AK3_230 - ECO 230 Economic Statistics Answer Key to...

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ECO 230 Marianna Kudlyak Economic Statistics Spring 2007 Answer Key to Homework #3 Total points: 10. Graded exercises: Ex.1 (2.5 points), Ex.3 (2.5 points), Ex. 6 (2.5 points). 0.5 points were added for the presence of each of the remaining 5 exercises. Exercise 1. Newbold, Carlson and Thorne, Problem 4.31 p.107. Let A be the event ‘no graduate student is selected’ The number of combinations of 3 chosen from 6 (2 graduate and 4 undergraduate students) is C 6 3 = 6!/(3!(6-3)!) = 6*5*4/(3*2) = 20 The number of combinations of no graduate student in the subcommittee: C 4 3 C 2 0 = (4!/(3!*1!)) (2!/(0!*2!)) = 4*1 = 4 P(A) = 4/20 = 1/5 Exercise 2. Newbold, Carlson and Thorne, Problem 4.35 p.107. Exercise 3. Newbold, Carlson and Thorne, Problem 4.37 p.107. a. Given that investors wants to invest in 2 U.S. funds (out of 6 available) and 2 international funds (out of 4 available): C 6 2 = 6!/(2!4!) = 6*5/2 = 15 C 4 2 = 4!/(2!2!) = 4*3/2 = 6 Because the selections are independent, there are 15*6 = 90 different sets of funds from which to choose. b. P (‘at least one fund in the selection underperforms’) = 1 – P (‘no fund in the selection under performs’) = 1 – P (‘no U.S. fund in the selection underperforms’ ‘no international fund in the selection underperforms’) Assuming that US and international funds perform independently, P (‘no U.S. fund in the selection underperforms’ ‘no international fund in the selection underperforms’) = P (‘no U.S. fund in the selection underperforms’)*P(‘no international fund in the selection underperforms’) P (‘no U.S. fund in the selection

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AK3_230 - ECO 230 Economic Statistics Answer Key to...

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