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quiz03_review_1

# quiz03_review_1 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Civil and Environmental Engineering 1.017 Computing and Data Analysis for Environmental Applications Practice Quiz 1, 2003 Problem 1 (Descriptive Statistics) During the manufacture of links in a chain, they are sampled at random and the tensile strength measured. Characterize the set of 12 maximum load values given below by plotting or computing the following descriptive statistics: Histogram Sample cumulative distribution function (CDF) Sample mean Sample standard deviation Sample median 6.2 3.8 5.0 4.8 3.4 5.3 3.9 6.4 4.2 5.5 5.2 4.0 Use the sample CDF to estimate the probability of a link having a tensile strength less than or equal to 4. Solution: Histogram: Mean = 4.8 Standard Deviation = 0.96 Median = 4.9

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CDF: P(strength<=4) = 4/12 = 0..33 Problem 2 (Combinations and Virtual Experiments) A geologic formation consists of 9 layers: 4 shale, 3 sandstone, and 2 limestone. We presume that these layers were laid down at random. Now suppose that we drill a borehole through the top 3 layers. What is the probability that these sampled layers are all
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quiz03_review_1 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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