Assign 7 - pmax function which takes the maximum value...

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Math 151, Spring 2011 Jo Hardin, HW #9 Homework due on Thursday, March 24 th , start of class. Note: we won’t cover 3.10 or the ideas about the Jacobian from 3.9. 1. DeGroot (3 rd or 4 th ed.), section 3.9: # 2, 4, 5, 7, 8 2. Can you form a triangle? Let A, B, and C be independent random variables uniform on [0, 1]. What is the probability that three sticks of length A, B, and C can form a triangle? (a) In R, simulate the above situation. According to your simulation, how often does there exist a triangle? [As always, if you want help with R, tell me exactly what you want to do, and I’ll tell you how to do it in R.] You may want to use the
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Unformatted text preview: pmax function which takes the maximum value element-wise in an array. > vector1 <- c(1, 7, 8, 1, 2) > vector2 <- c(1, 4, 1, 2, 3) > max(vector1, vector2) > [1] 8 > pmax(vector1, vector2) > [1] 1 7 8 2 3 (b) Analytically: find the probability that three random U[0,1] sticks will form a tri-angle. [Hint: the easiest way I found to do this was to start by assuming one of the values (say C ) was the biggest one. Then to generalize I realized that any of the values could have been the biggest one. It is much harder to approach this problem using the theory of order statistics.]...
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This note was uploaded on 02/17/2012 for the course MATH 151 taught by Professor Jo.h during the Spring '10 term at Pomona College.

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