Homework 3

Due Monday September 24 at 11:59pm

Homework policies and submission instructions

Problems

  1. (5 points) Textbook problem 3.8
  2. (10 points) Textbook problem 3.19. Express your answers as products of fractions or using choose notation. There's no need to compute numerical answers.
  3. (15 points) Textbook problem 3.27. Express your answers using choose and/or summation notation. There's no need to compute numerical answers.
  4. (10 points) Suppose that a student is registered this semester in Math 225 (course explorer) and CS 361 (course explorer). In this problem, you will think about the student's registration in combinations of sections of these two classes. Assume that the student's other classes do not conflict with any sections of Math 255 or CS 361.
    1. Write down the sample space of all valid non-conflicting registrations in Math 225 and CS 361. Use the following notation: \( (TL1, AL1, ADF) \) is the outcome that means the student is in Math 225 TL1 and CS 361 AL1 and ADF.
    2. Now assume that the outcomes you listed in part (a) are equally probable. Let \( E_{SL1} \) be the event that the student is registered in Math 225 SL1, and so on for other sections.
      1. Are \( E_{SL1} \) and \( E_{AL1} \) independent? Justify your answer with calculations.
      2. Are \( E_{SL1} \) and \( E_{ADB} \) independent? Justify your answer with calculations.
      3. Are \( E_{TL1} \) and \( E_{ADF} \) independent? Justify your answer with calculations.
  5. (10 points) Go to this grade disparity data visualization and look up the data for ECE 120: Introduction to Computing. Consider a randomly selected former ECE 120 student whose data is represented in this data set. Let \( A \) be the event that the student received some type of A grade. Let \( V\) be the event that the student had David Varodayan as ECE 120 instructor.
    1. Before doing the calculations below, determine whether \( P(V|A) \) is going to be smaller or larger than \( P(V) \). In one sentence, explain in words why you think so.
    2. Calculate \( P(V) \).
    3. Calculate \( P(V|A) \).
    4. What assumption about the data (that is not actually true) did you have to make to perform the calculations above? Hint: ECE 120 is a prerequisite for many other ECE classes.