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homework_06

# homework_06 - Î =70 storms/year The rainfall intensity I of...

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MIT OpenCourseWare http://ocw.mit.edu 1.010 Uncertainty in Engineering Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.

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1.010 Fall 2008 Homework Set #6 Due October 28, 2008 (in class) 1. A chain has 10 links. The strengths of the links, X 1 , …, X 10 are independent and identically distributed random variables with exponential PDF f X ( x ) = e - x , x 0 Find and plot the PDF of the strength of the chain S = min{ X 1 , X 2 , …, X 10 }. Is the distribution of S also exponential? 2. At a certain location storms arrive as a Poisson point process with rate
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Unformatted text preview: Î» =70 storms/year. The rainfall intensity I of each storm has CDF P [ I â‰¤ i ] = F I ( i ) = 1-e -0.067 i , i â‰¥ 0 where i is in mm/hour. Assuming independence among the storm intensities, find the probability that the yearly maximum rainfall intensity exceeds 100mm/hour. [Read application example 11.] 3. U 1 and U 2 are independent random variables with uniform distribution in [0,1]. Find the CDF of Y = U 1 + U 2 . Then differentiate F Y (y) to find the PDF, f Y (y). [Hint: To find F Y (y) , sketch the region " y on the ( U 1 , U 2 ) plane where Y " y .]...
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• Spring '05
• GeorgeKocur
• Probability theory, CDF, Poisson point process, rainfall intensity, maximum rainfall intensity, certain location storms

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