# hw3 - obtained independently each of size N = 50 1 For...

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ChE/MEE 138 — ChE/MEE 212 (F2000) THE PRINCIPLES OF RISK ANALYSIS Homework #3 The purpose of this homework is to get a deeper understanding of (a) the law of large numbers, (b) the First Limit Theorem and (c) the Central Limit Theorem, by employing them to the data from a virtual experiment. The experiment is a sampling from an unknown (to you) population. After you submit your results, the population will be revealed to you. Also, in this homework, we create an opportunity to learn to use and appreciate the value and meaning of a ” sampling distribution. You will receive by e-mail (Microsoft Excel spreadsheet format) the sample data as follows: (i) Six independent data sets, of varying sizes: N = 10, 20, 30, 40, 50 and 60, (ii) Thirty data sets,
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Unformatted text preview: obtained independently, each of size N = 50 . 1. For the (i) data sets, determine and plot the means and variances, as functions of N . Discuss. 2. From the results in 1, estimate the population mean ( ), and standard deviation ( ). Plot the sampling distribution of the means ( M ) for N = 50 . 3. Take the sampling distribution you just did, and check it against the data in set (ii). Comment. 4. Use all the data in (ii) to construct an approximate, discrete probability distribution of the population. Then use the data sets in (i) to examine how the frequency of a particular event (your choice) behaves in light of the First Limit Theorem....
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