Assignment 12

Assignment 12 - University of California Berkeley Fall...

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University of California, Berkeley Department of Mechanical Engineering Fall Semester 2008 Instructors: M. Frenklach, R. Horowitz E7, Assignment 12 Assigned: Tuesday, December 3, 2008 Due: 12:00 pm (noon), Wednesday, December 10 , 2008 This assignment is on statistics, numerical differentiation, integration, and solution of ordinary differential equations. As before, turn in the hard copy of your published file to the drop boxes in Etcheverry 1109 and upload the soft copies of your script and your functions (the M-files) to bspace. Do not forget to name your main M-file as lastname_firstname_SID_lab12.m NOTE: Do not forget to display the contents of your user-defined functions using the command type. MATLAB commands * introduced in this assignment: mean, std, bar, erf, erfc, quad 1. A package delivery company (such as FeDex or UPS) has 500 planes departing from one of its hubs and each plane is loaded with 10,000 packages. The weight of each package can be considered as a uniformly distributed independent random variable between 2 kg and 10 kg. a) Calculate the mean and standard deviation of the weight of each package. Hint: Define the weight of a package by W . Since each weight W is uniformly distributed between 2 kg and 10 kg, then the probability distribution function (PDF) of the package weigh is 1 for 2 10 () 8 0 elsewhere w w pw = Therefore, as discussed in Lecture Notes 23 - Statistics, the mean W μ and standard deviation W σ of each package are respectively given by 10 22 2 11 1 0 2 1 0 6 (10 2) 2 10 2 2 WW wp w dw wdw −∞ −+ == = = −− ∫∫ 2 = * Please refer to MATLAB help to learn how to use the functions introduced in this assignment. Assignment 12 E7 1
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University of California, Berkeley Department of Mechanical Engineering Fall Semester 2008 Instructors: M. Frenklach, R. Horowitz 10 22 2 2 2 2 1 () ( ) ( ) 6 (10 2) WW W wp w d w w p w d w w d w σμ μ ∞∞ −∞ −∞ =− = = = ∫∫ 2 ? Complete the right hand side of the second equation. b) Calculate the mean and standard deviation of the total weight L that each plane must carry. Hint: Since each plane carries 10,000 packages, and the weight of each package is an independent random variable with mean W and standard deviation W σ , then, as discussed in Lecture Notes 23 - Statistics, the mean and standard deviation of the total plane load L, L and L , are 10000 LW =⋅ and 2 10000 σσ c) The following MATLAB command generates a 500×1 array L, where the kth element L(k) is a randomly generated number that simulates the load L k carried by the kth plane. >> L = sum(8*rand(500,10000)+2,2); i) Use the MATLAB commands mean and std to respectively determine the sample mean and standard deviations 500 1 1 500 k L = = L k and 500 2 1 1 (() ) 500 L k Lk L = and respectively compare them with theoretical values L and L calculated above.
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This note was uploaded on 11/01/2009 for the course ENGLISH 7 taught by Professor Sengupta during the Spring '09 term at Berkeley.

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Assignment 12 - University of California Berkeley Fall...

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