AK4_230 - ECO 230 Marianna Kudlyak Economic Statistics...

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Unformatted text preview: ECO 230 Marianna Kudlyak Economic Statistics Spring 2007 Answer Key to Homework #4 Total points: 10. Graded exercises: Ex.2 (2 points), Ex.3 (2 points), Ex. 5 (2 points), and Ex. 8 (2 points). 0.5 points were added for the presence of each of the remaining 4 exercises. Exercise 1. Newbold, Carlson and Thorne, Problem 4.111 p.130. Exercise 2. Consider the random experiment of rolling two dice at the same time. a) What is the sample space? Basic outcome: (x;y); where x is the number from the first die and y is the number from the second die. Then sample space consists of 36 possible outcomes: S = {(1;1) (2;1) (3;1) (4;1) (5;1) (6;1) (1;2) (2;2) (3;2) (4;2) (5;2) (6;2) (1;3) (2;3) (3;3) (4;3) (5;3) (6;3) (1;4) (2;4) (3;4) (4;4) (5;4) (6;4) (1;5) (2;5) (3;5) (4;5) (5;5) (6;5) (1;6) (2;6) (3;6) (4;6) (5;6) (6;6)} b) Construct a discrete random variable X. There are no restrictions, you are free to build it as you like, as long as it is a valid random variable. Answers vary. One of the possibilities: Let X equals 1 whenever the sum of the numbers of the outcome is odd number, and 0 otherwise. Hence, X((2;1);(4;1);(6;1);(1;2);(3;2);(5;2);(2;3);(4;3);(6;3)(1;4);(3;4);(5;4);(2;5);(4;5); (6;5);(1;6);(3;6);(5;6)) = 1 X((1;1);(3;1);(5;1);(2;2);(4;2);(6;2);(1;3);(3;3);(5;3);(2;4);(4;4);(6;4);(1;5);(3;5); (5;5);(2;6);(4;6);(6;6)) = 0 c) What is the probability distribution function of the random variable X that you constructed? What is the cumulative distribution function of X? Assuming that dice are fair, the probability of each basic outcome in the sample space is 1/36. Hence, probability distribution function of X: x i P(X = x i ) 0 18/36 1 18/36 Or P(X = x) = for x = 0;1 Cumulative distribution function: F(x i ) = 0 if x i < 0 F(x i ) = 1/2 if 0<= x i <1 F(x i ) = 1 if 1<= x i d) Graph pdf and cdf of X....
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This note was uploaded on 06/09/2008 for the course ECO 230 taught by Professor Kudlyak during the Spring '08 term at Rochester.

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AK4_230 - ECO 230 Marianna Kudlyak Economic Statistics...

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