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quiz01_3sol

# quiz01_3sol - 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 3 December 5, 2001 Please answer all questions on a separate piece(s) of paper with your name clearly identified: Problem 1 (15 points) Provide a brief answer to each of the following questions: a) Suppose that you have a choice of collecting a random sample of 20, 40, 80, or 160 measurements of a random variable y . You will use the sample to compute the sample mean m y , which you will use as an estimate of E [ y ]. Draw a sketch of the probability density of m y for n = 20 measurements and superimpose on it a sketch of the same density for n = 40 measurements. b) Plot the standard deviation of the sample mean vs. the number of measurements in the sample. How does the standard deviation at n = 160 compare to the standard deviation at n = 20? c) Is the sample mean a consistent estimate of E [ y ]? Why? Solution: a) Plot should look normal. Standard deviation for n = 40 should be 0.70 standard deviation for n = 20, peak for n = 40 should be 1.41 peak for n = 20. b) Standard deviation of sample mean should decrease as n -1/2 . c) Yes, because Lim 0 ] [ = y n m Var Problem 2 (25 points) You are studying the cadmium concentration ( y ) in trout tissue in a large lake. You catch ten trout and measure the following cadmium concentrations (mg/L): 0.106 0.040 0.128 0.225 0.167 0.024 0.317 0.072 0.099 0.029 a) Considering the possible values of the data, what would be a reasonable assumption for

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quiz01_3sol - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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