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Exam 3 in EE 300, Fall 2007: Statistical Analysis and Linear Algebra - Prof. Jon R. Marstr, Exams of Electrical and Electronics Engineering

University of Alabama - BirminghamElectrical and Electronics Engineering
Prof. Jon R. Marstrander

The instructions and problems for exam 3 in ee 300, a university course offered in fall 2007. The exam covers statistical analysis, including calculating means, standard deviations, and confidence intervals for a dataset of height and weight measurements. It also includes problems on linear algebra, such as performing gauss elimination on systems of linear equations and finding the inverse of a matrix.

Typology: Exams

Pre 2010

Uploaded on 04/12/2010

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EE 300, Fall 2007, Exam 3 (Take Home)
15 November 2007 Page 1 / 14
Name: __________________________________________
First, please sign the statement below, indicating your agreement. You must sign this
statement to receive credit for the exam.
I agree that in return for the trust that has been placed in me by allowing me to
take this exam outside of normal class time, that I have maintained the highest
ethical standards. I have not communicated in any way with anyone other than
the course instructor about the content of this test, nor solutions to any of its
problems, nor have I copied from anyone. I have followed the rules below. On my
honor, the work presented is my own.
Signature: __________________________________________ Date: ______________
You may use calculators, pens and pencils, books, MATLAB, EXCEL, and your brain.
If you use MATLAB or EXCEL, you should include printouts of this work.
You may NOT work with anyone else on this exam. You may NOT post questions nor
receive answers regarding this exam via email, discussion boards, nor forums of any
kind. Do not discuss this test with anyone until both of you have handed-in your papers.
This is a test of what you know.
Show All Work. Simply presenting an answer is NOT sufficient. Attach extra paper if
needed. Clearly label all work done outside of the indicated areas. Clearly indicate your
final answers.
The Exam is due by 11:59 pm on Wednesday 21 November, 2007. You may submit a
paper version to me personally, slide a paper copy under my office door, or email me an
acrobat PDF file, by this time.
After you have finished the exam, please answer the following questions. They will
NOT affect your grade.
What grade do you think you made on this exam: ________
How difficult is this exam? (10 = way too hard, 0 = way too easy): ________
Comments:
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Download Exam 3 in EE 300, Fall 2007: Statistical Analysis and Linear Algebra - Prof. Jon R. Marstr and more Exams Electrical and Electronics Engineering in PDF only on Docsity!

EE 300, Fall 2007, Exam 3 (Take Home) 15 November 2007 Page 1 / 14

Name: __________________________________________ First, please sign the statement below, indicating your agreement. You must sign this statement to receive credit for the exam. I agree that in return for the trust that has been placed in me by allowing me to take this exam outside of normal class time, that I have maintained the highest ethical standards. I have not communicated in any way with anyone other than the course instructor about the content of this test, nor solutions to any of its problems, nor have I copied from anyone. I have followed the rules below. On my honor, the work presented is my own. Signature: __________________________________________ Date: _________ You may use calculators, pens and pencils, books, MATLAB, EXCEL, and your brain._____ If you use MATLAB or EXCEL, you should include printouts of this work. You may receive answers NOT (^) work with anyone else on this exam. You mayregarding this exam via email, discussion boards, nor forums of any NOT post questions nor kind. Do not discuss this test with anyone until both of you have handed This is a test of what you know. -in your papers. Show All Work. needed. Clearly label all work done outside of the indicated areas. Clearly indicate your final answers. Simply presenting an answer is NOT sufficient. Attach extra paper if The Exam is due by 11:59 pm on Wednesday 21 November, 2007. You may submit a paper version to me personally, slide a paper c acrobat PDF file, by this time. opy under my office door, or email me an After you have finished the exam, please answer the following questions. They will NOT affect your grade. What grade do you think you made on this exam: ________ How difficult is this exam? (10 = way too hard, 0 = way too easy): ________ Comments:

You have been hired by a public health agency to study the relation betw height and weight. They have taken a properly randomized sample of people, and measure their height and weight. The results of this study are listed in the table below.een a person's Each line in the table represents the data for a single individual fr your data set for all of the statistical analysis you will perform on this test.om the sample. This is Height (inches) 6672 Weight (pounds) (^148172) (^687071 ) (^736970 ) (^697072 ) (^707168 ) 716970 161771767 (^697270 )

2 b) [5 points] Compute a point estimate of the stan population, based on the sample data. dard deviation of height for the entire

  1. [10 points] Compute a confidence interval for the mean of h population, to a 95% confidence level, based on the sample data. Be sure to state your assumptions, identify your procedure, and clearly indicate the steps in your work, andeight for the entire indicate your final answer.
  1. [10 point based on the sample data? What does this correlation value indicate?s] What is the correlation between the height and weight for this population,

Bonus(!) [5 points] Is the correlation in problem 6 significant to a 90% confidence level?

  1. [30 points, 10 points each] Perform Gauss Elimination on the following systems of simultaneous linear equations.
    • • • If a unique solution exists, find it.If no solution exists, state thatIf an infinite number of solutions exist, state the dimensionality of the solution 7 a) [10 points]^ space.

12 ww ++ 34 x^ x +^ " 21 yy^ "+^17 zz =^ = 28 25 1 " w^1 w "^ + 2 x^2 x +^ " 5 y^3 y +^ + 0 z^4 = z^ = 3 "^3

7 b) [10 points]

13 ww ++ 17 xx^ ++^214 y^ y + "^2 6 z^ z = =^6 " " 12 ww ++ (^21) xx ++ 24 yy "" 33 zz == 1 5

  1. [10 points] Represent the following set of simultaneous equations in matrix form (Ax=b), and then try to invert the matrix A using Gauss inverse exists, solve for x using this inverse. -Jordon elimination. If the

" " 513 x (^1) x 1 + + 2 15 x (^2) x + 2 2 + x 73 x = 3 2 = 65 " 2 x 1 + 2 x 2 + 1 x 3 = 8

  1. [5 points] Perform the indicated operations on the following matrices. If the operation is undefined, you should state that.

!

A = ( 1 3 " 1 )

B =^ " #^ $ $ $ 123 % &^ ' ' '

C =^ # $^ % % % "^142 " 131 "" 123 & '^ ( ( (

D =^ " #^ $ $ $^146 072 031 % &^ ' ' '

E =^ # $^ % % % " 14134 "^012 "^073 & '^ ( ( (

a) [1 point] Find AC b) [1 point] Find BA c) [1 point] Find A*B d) [1 point] Find D+A e). [2 point] Find the rank of D