ELEC 471, Fall 2010
Prof. Rich Kozick

Homework 10


Date Assigned: Monday, November 26, 2010
Date Due: Wednesday, December 1, 2010 at 3:00 PM

  1. Reading: Please continue to study Chapter 3 on continuous random variables, with emphasis on derived random variables (cdf, pdf, expected value) and Gaussian random variables. This is the final homework assignment, but the final exam will include material that we cover through class on Friday, December 3. Final Exam: Please refer to the final exam link Announcement on Blackboard.

  2. Please solve the following problems at the end of Chapter 3 along with item 4 below, and submit solutions at 3:00 PM on December 1.
    Section 3.3: 1 (Note that you do not have to find the pdf of Y to answer this).
    Section 3.4: 5 and 7 (note that X is an exponential random variable and use Appendix A for the mean and variance).
    Section 3.5: 1.
    Section 3.7: 5.

  3. Suppose that X and Y are two variables that can be approximately described by the linear function Y = a X for some value of the constant a. Your job is to determine or "estimate" the value of a from the following five pairs of measurements of (X, Y): 
       X         Y
  ---       ---

 1.00     0.688
 1.78     0.849
 3.16     2.152
 5.62     3.024
10.00     5.453
    A MATLAB program hw10.m is linked to this assignment on the web page. The MATLAB program plots the data values, and it also allows you to plot the "fit" provided by the equation Y = a X for values of the parameter a that you set in the program.

    What do you think is the "best" estimate of the parameter a to fit the given data with the relation Y = a X? Justify your answer as quantitatively as you can. Explain exactly how you arrived at your choice of a. Note that there is not a single correct answer, but there are many incorrect answers!

  4. We will have a short quiz on December 1 at 3:00 PM that will introduce you to least-squares estimation. You will be guided through the quiz so you do not need to study.

  5. Presentations: The following students are asked to present their solutions on December 1 at 3:00 PM.
Thank you.