mini_quiz_4

mini_quiz_4 - m V = miles 60 hour and standard deviation σ...

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MIT OpenCourseWare http://ocw.mit.edu 1.010 Uncertainty in Engineering For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Fall 2008
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1.010 – Mini-Quiz #4 (40 min – open books and notes) Problem 1 (30 Points) Consider two variables X 1 and X 2 , each with possible values –1 and 1. The joint probability mass function of X 1 and X 2 is shown in the figure below. (Notice that the distribution is concentrated at four points, with equal probability 0.25 at each point) X 2 1 -1 X 1 0.25 0.25 0.25 0.25 1 -1 0 (a) Are X 1 and X 2 independent? (b) Are X 1 and X 2 uncorrelated? Justify your answers Problem 2 (30 Points) 50 The time T ( in hours) for a car to travel 50 miles of a highway is given by T = V , where V is the car speed in miles/hour. Suppose that V has mean value
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Unformatted text preview: m V = miles 60 / hour and standard deviation σ V = miles 10 / hour . Find in approximation the mean value and standard deviation of T. Problem 3 (40 Points) Consider the two columns shown in the figure below, where X 1 and X 2 are random load variables. 2X 1 X 1 X 2 Y 1 Y 2 The loads Y 1 and Y 2 at the base of the columns are given by: Y 1 = X 2 1 Y 2 = X 1 + X 2 Suppose that X 1 and X 2 have common mean value m and common standard deviation σ and denote by ρ their correlation coefficient. (a) Find the variances of Y 1 and Y 2 . (b) What effect does ρ have on the variance of Y 2 ? (c) Explain in intuitive ways the results for ρ = − 1 and ρ = 1 . Also compare with the variance of Y 1 . (Notice that for X 1 = X 2 the load on the two columns is the same)....
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This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.

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mini_quiz_4 - m V = miles 60 hour and standard deviation σ...

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