Engineering homework assignment

ENGR 201 Spring 2015 Biweekly Assignment 4 Due: Friday, May 22, 2015, 11:59:00 p.m. EST

ENGR 201: BIWEEKLY ASSIGNMENT 4 (WEEK 7-8)

Generating Distributions and varying Parameters (2 points)

Use probability density functions (easily available online) equations to provide information about the theoretical range and number of parameters of the following distributions. Further, generate pdfs as column charts for these distributions by implementing the PDF in excel (and not using the inbuilt excel functions). Vary the parameters to realize different shapes of the distributions.

1. Rayleigh 2. Poisson 3. Weibull 4. Log-normal

Distributions and Parameter Fitting (3 points)

The following dataset provides the number of times chemical instruments of a particular batch produced by a company experienced a technical glitch. It was found that 48 instruments did not experience any technical glitch, 37 instruments experienced 1 technical glitch, and so on.. For this dataset,

1) Identify a probability distribution that best describes the data with correct reasoning 2) Using the steps described in the lecture, estimate the parameter(s) of the distribution that

best fits the data. Specifically, a. Import the data into excel and indicate the name and probability distribution/mass

function (PDF/PMF) of the distribution you selected in Question 1 above. b. Calculate the probabilities P(X = x) using the (PDF/PMF) c. Calculate the log-likelihood by summing up the f_x*ln(P(X=x)) d. Use solver to Maximize the Log-Likelihood using appropriate constraints e. Visualize the results

x f_x 0 48 1 37 2 30 3 24 4 20 5 16 6 13 7 11 8 9 9 7 10 6 11 5 12 5 13 3 14 3

© Roger Marino, Ben Pelleg, Pramod Abichandani,, Drexel University

ENGR 201 Spring 2015 Biweekly Assignment 4 Due: Friday, May 22, 2015, 11:59:00 p.m. EST

15 2 16 2 17 2 18 1 19 1 20 2 21 1 22 1 23 1

Transportation Sector (4 points)

Use: http://www.epa.gov/otaq/fetrends-complete.htm Data sets in appendices: http://www.epa.gov/fueleconomy/fetrends/1975-

2013/420r13011-report-tables.xlsx 1. Highlight the vehicle fuel economy trends in the U.S. from 1975-2011 2. Highlight the trends in CO2 emission (in g/mi) in the U.S. due to vehicle emissions from 1975-

2011 3. Is there a correlation between the fuel economy and CO2 emissions? Explain your findings. 4. Using historical gas prices in the state of PA, ascertain the maximum and minimum gas prices

between 1983-2010. http://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=PET&s=EMA_EPM0_PTC_SPA_DPG&f=M

5. Use curve fitting to appropriate subsets of the data to ascertain gas prices for 1975 to 1982 and 2011.

6. Using the average gas price per year, is there a correlation in PA gas prices and U.S. CO2 emissions between 1975-2011? Explain your findings.

7. Given your findings about vehicle fuel economy and CO2 emissions in US, propose one improvement to reduce CO2 emissions due to the transportation sector? In your answer, discuss the rationale and pros and cons of your suggested solution. Please cite your sources of information.

Final Project Data (1 point) Find at least two data sets that you will analyze for your final project policy. Import these data sets into Excel and do a basic descriptive statistics analysis (count, max, min, avg, etc.). In the summary tab, write a paragraph explaining interesting features of the data and how you will be using the data for your policy. Make sure the source of the data is clearly labeled.

© Roger Marino, Ben Pelleg, Pramod Abichandani,, Drexel University

ENGR 201 Spring 2015 Biweekly Assignment 4 Due: Friday, May 22, 2015, 11:59:00 p.m. EST

Biweekly Assignment 4 Specification Sheet

Overall Specifications: 1. Students are encouraged to explore material beyond the lecture slides and links provided in this

assignment. 2. Please provide references for all the material used for this assignment. 3. All statistical analyses should be contained in different sheets of the same Excel Workbook with

answers and functions/methods used clearly indicated on every sheet. 4. All summary descriptions/explanations should be included in the first sheet of the Excel Workbook

(no page limit, but be reasonable). 5. Provide ample visualizations with appropriate labels and annotations (as listed in rubric

description). Generating Distributions and varying Parameters

1. Use the mathematical equations for PDFs to generate the PDF and visualize them as column charts 2. Provide the range and the number of parameters 3. Make sure that you can change the parameters to see how their values affect the distribution

Transportation Sector

• Use Excel functions to calculate specified descriptive statistics for Question 3. For other questions create the following appropriate visualizations as necessary:

o Time series analysis with smoothing o Curve fitting and extrapolation o Correlations and linear regressions

How to submit this assignment? • Name it using the following convention: Section##Group**Biweekly4

a. ## is your section number b. ** is your group number

• Upload your assignment to BbLearn by Friday, May 22, 2015, 11:59:00 p.m. EST • Groups that upload the assignment before 8:00 p.m. EST on Friday, May 22, 2015 will get 0.5 extra points on

the final grade (see syllabus) • Incorrect naming of your Excel file will result in a deduction of 1 point

© Roger Marino, Ben Pelleg, Pramod Abichandani,, Drexel University