Question

Problem 4. The following data are the temperatures (in degree Fahrenheit) of effluent at discharge from a sewage treatment facility on consecutive days: 43 47 51 48 52 50 4649 45 52 46 51 4444651 59 45 44 50 48 50 49 50 Using the Method of Moments, fit a normal distribution, a lognormal distribution, an exponential distribution, and a uniform distribution and provide the following for each distribution: a. Parameters of the distribution. Using the fitted distribution, find the probability that temperature exceeds 58 °F? Using the fitted distribution, find the temperature value that is exceeded only 5% of the time. Graphically evaluate the goodness-of-fit of the distributions using: (1) the overlay of eCDF and CDF of the distributions; and (2) the probability plots for the distributions [you can use the "probplot" function in MATLAB). Based on visual evaluation, do these distributions fit the temperature data? b. c. d. Show all of the probability plots on the same figure. Summarize the results in a table similar to Table 1. Show the equations for computing the parameters of the fitted distributions. You must show all equations and procedures for answering these questions. You can use MATLAB only to confirm the accuracy of your procedures or to create figures. Table 1. Summary results for Problem 4 Distribution Parameter Parameter 2 P(T>58叨 T095( Normal Lognormal Exponential Uniform 48.5 F ơ 3.5 F 0.0033 54.26 ω ? a -?

Answer 1

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