Homework
Homework exercises will be assigned weekly and posted below. For a pdf copy, click here. You are expected to know how to do all of the exercises presented. Voluntary discussion meetings will be held on Mondays, and online help is available through Piazza. See the help page for more details.
- Exercises for Tuesday, January 27 (due Week 2):
- Chapter 1: Problems (pg 15ff): 8, 10, 11, 13, 16, 18, 25, 27, 28, 30
- Chapter 1: Theoretical Exercises (pg 17ff): 8 (see note below), 13, 16, 17 (see note below)
- Note: For theoretical exercise #8, interpret "prove" as "give a convincing argument." For theoretical exercise #17, interpret "combinatorial argument" as "explain why you expect this to be true by a counting example, rather than just the mathematical algebra."
- Exercises for Tuesday, February 10 (due Week 3):
- Exercises for Tuesday, February 10 (due Week 4):
- Chapter 2: Problems (pg 48ff): 2, 4, 8, 9, 12, 15, 19, 23, 25, 31, 36, 38, 41, 43, 45
- Chapter 2: Theoretical Exercises (pg 52ff): 9, 11, 13
- Exercises for Tuesday, February 17 (due Week 5):
- Chapter 3: Problems (pg 97ff): 1, 4, 5, 11, 14, 17, 24, 27, 29, 32, 39, 40, 44
- Chapter 3: Theoretical Exercises (pg. 106ff): 2, 5
- Exercises for Tuesday, February 24 (due Week 6):
- Chapter 3: Problems (pg 97ff): 41, 51, 53, 54, 66, 70, 81
- Chapter 4: Problems (pg 163ff): 1, 2, 5 (see note below), 7 (see note below), 13
- Note: For #5 and #7, when the book says, "what are the possible outcomes..." for a particular random variable, I want you to read it as, "what is the state space of ..." that particular random variable.
- Exam 1 Study Guide/Tips: All questions listed above are fair game. In addition, any quiz, homework, or example problem has a chance of being on the exam. I also strongly suggest you work through the review questions at the end of each chapter as well.
- Exercises for Tuesday, March 3 (due Week 7):
- Chapter 4: Problems (pg 163ff): 17, 18, 19, 20(a), 20(b), 40 (see note below), 60
- Note: For #40, you can likely answer this without the "technology" of random variables; however, try and use the random variable technology to get used to it. In particular, if X is the (random variable giving the) number of correct answers the student gets while guessing, then convince yourself that X = Bin(n,p) for a good choice of n and a good choice of p.
- Exercises for Tuesday, March 10 (due Week 8):
- Chapter 4: Problems (pg 163ff): 20c, 25, 30, 32, 33, 35, 37, 38, 41, 51, 53, 58
- Chapter 4: Theoretical Exercises (pg 163ff): 3, 6, 19
- Exercises not from Ross: See here under Week 8.
- Exercises for Tuesday, March 17 (due Week 9):
- No exercises: Spring break!
- Exercises for Tuesday, March 24 (due Week 10):
- Chapter 4: Problems (pg 163ff): 52, 54, 55, 57, 72, 79
- Chapter 4: Theoretical Exercises (pg 163ff): 20
- Chapter 5: Problems (pg 212ff): 1, 2, 3, 4, 7, 10, 11, 12, 13
- Exercises not from Ross: See here under Week 10.
- Exercises for Tuesday, March 31 (due Week 11):
- Chapter 5: Problems (pg 212ff): 15 (see note below), 17, 18 (see note below), 19 (see note below), 21 (see note below), 23, 25, 26, 27, 28, 32, 33, 40, 41
- Chapter 5: Theoretical Exercises (pg 214ff): 1, 9 (see note below), 10, 15, 31
- Exercises not from Ross: See here under Week 11.
- Note:
- For both #15 and #17, leave your answer in terms of Φ. For the second question in #21, it is asking for you to condition on the event that the height is ≥ 6 feet.
- The CDF Φ of a standard normal random variable is invertible on the range (0,1). That is, if for some 0 < y < 1 you have an expression of the form Φ(x) = y, you can solve for x by x = Φ^{-1}(y) (where Φ^{-1} is the inverse of Φ, not 1/Φ). Therefore, if you don't want to use the table of values for Problems #18 and #19, you can leave your answer in terms of the inverse Φ^{-1}.
- For Theoretical Exercise #9, when the book says "show," what I want you to do is to draw a sketch of the density of Z and convince yourself that the equalities are true by shading in the appropriate areas.
- Exercises for Tuesday, April 7 (due Week 12):
- Chapter 6: Problems (pg 271ff): 2, 4
- Do all of Exam 2 practice problems
- Exercises for Tuesday, April 14 (due Week 13):
- No exercises: Exam recovery!
- Exercises for Tuesday, April 21 (due Week 14):
- Chapter 6: Problems (pg 271ff): 8, 9, 10, 13, 14, 15, 20, 23, 26, 27
- Exercises not from Ross: See here under Week 14.
- Exercises for Tuesday, April 28 (due Week 15):
- Chapter 6: Problems (pg 271ff): 28, 38, 45, 56
- Chapter 7: Problems (pg 352ff): 4, 12, 16, 30, 37, 45, 75
- Chapter 7: Theoretical Exercises (pg 359ff): 19
- Exercises not from Ross: All exercises in the Covariance and Correlation Notes
- Last exercises for Finals Week: