cee93-fall07-mt-Hansen-soln

cee93-fall07-mt-Hansen-soln - CE93 Midterm Solutions,...

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CE93 Midterm Solutions, October 30, 2007; Posted November 26, 2007 Prepared by Megan Smirti Problem 1: Occupancies of 100 vehicles driving in the HOV lane of the East Shore Freeway are observed. The results are summarized in the table below. Occupancy (persons in vehicle) Number of Vehicles 1 20 2 50 3 20 4 5 5 5 a) Draw a histogram for these data. b) Draw a cumulative frequency diagram for these data. c) Draw a box and whiskers plot for these data. d) What is the median occupancy? e) What is the variance of the occupancy? f) Is the skewness of the occupancy positive or negative? Explain. g) Does the variability in occupancy reflect aleatory or epistemic uncertainty? Explain a) 0 10 20 30 40 50 60 12345 Occupancy # Occurances b)
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CE93 Midterm Solutions, October 30, 2007; Posted November 26, 2007 Prepared by Megan Smirti c) note – the outlier at 5 represents 5 data points d) median is where F x (x) = .5 Æ x. 5 = 2 e) Var (X) = E(X 2 ) – E(X) 2 E(X) = 1 * 0.2 + 2 * 0.5 + 3 * 0.2 + 4 * 0.05 + 5 * 0.05 =2.25 E(X 2 ) = 1 2 * 0.2 + 2 2 * 0.5 + 3 2 * 0.2 + 4 2 * 0.05 + 5 2 * 0.05 =6.05 Var (X) = 6.05- 2.25 2 =.988 f) The skewness is positive. There are more possible values of occupancy to the right of the expected value. Also, the box and whiskers plot shows 5 outliers in the right tail of the distribution. g) Aleatory uncertainty, or uncertainty associated with randomness, characterizes the variability of occupancy. This is because occupancy is a random variable, and as we collect occupancy data, we expect randomness. Epistemic uncertainty is uncertainty in knowledge – we have no reason to expect this uncertainty when collecting occupancy data.
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This note was uploaded on 07/11/2009 for the course CEE cee taught by Professor Monteiro during the Fall '05 term at University of California, Berkeley.

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cee93-fall07-mt-Hansen-soln - CE93 Midterm Solutions,...

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