Fall, 2018







Lecture 
Date 
Lecture & Lab Topics 
Readings Prob = "Schaum's Outline of Probability" MCS = "Mathematics for Computer Science" 
Practice Problems, Homeworks, and Tests 
Labs 

1  T 9/4  Administrative matters; Goals of the course; Motivating Examples: Why should you know probability and statistics? Probability and Statistics as the science of quantifying uncertainty. What is randomness? Probability and Computer Science. Lecture Slides: PDF 
Just for Fun: Here is a short YT video with various clips from movies which involve probability (we will return to the Monty Hall Problem, the first clip, soon): HTML Here is a nice exploration of the nature of randomness and our perceptions: HTML 

2  Th 9/6  Basic definitions of probability theory: outcomes, sample spaces, probability functions, axioms for probability functions; examples of finite, countably infinite, and uncountable sample spaces and typical problems in each. Probability functions for finite, equiprobable spaces, and extention to uncountable case. Anomalies arising from infinite sample spaces. 
Read through Ch. 1 & 2 in Prob if you need a review of the basic math background. Prob Sections 3.1  3.5. 
Practice problems from Prob (not to hand in): 3.2, 3.3, 3.5, 3.6, 3.7, 3.16, 3.18, 3.26. HW 01: IPYNB: due Th 9/13 @ midnight HW 01 Solution: PDF YT Instructions for converting IPYNB to PDF: PDF 

M 9/10 
Lab 01: IPYNB (Jupyter Notebook  right click and select Save Link As...). Due Th 9/13 @ midnight along with HW 01. Lab 01 Solution: PDF 

3  T 9/11  Set operations on events and axiomatic method for proving theorems about probability functions; nonequiprobable probability spaces.  Same readings as last time; also read MCS sections 17.1 & 17.2 on the "Monty Hall Problem" and the "Four Step Method." Look at the link above to a video of the "Monty Hall Problem." Optional: Section 17.5 from MCS covers the same material in Prob Chapter 3, but more rigorously, it is worth looking at for the application of the tree diagram technique. Optional: Section 4.3 of Prob has a slightly different presentation of the tree diagram technique. Prob p.94 has a nice explanation of trees resulting from independent trials (the simplest case).

The practice problems listed in the previous row apply to this lecture as well.


4  Th 9/13  Problem solving strategies; analysis using tree diagrams and the "Four Step Method"; the inverse method. Example: The Monty Hall Problem. Conditional Probability; Independence. 
Prob, Ch.4. MCS 18.5  18.7 has the same material. 
Practice problems from Prob (not to hand in): 4.1, 4.4, 4.5, 4.6, 4.21, 4.22, 4.25, 4.26, 4.29, 4.36 Tree diagram problems from Prob: 2.32, 2.33 HW 02: ZIP (due 9/20 @ 11:59pm) Solution: PDF


M 9/10 
Lab 2 Problem Set: ZIP 

5  T 9/18  Independence reviewed; Bayes' Rule. Counting principles and combinatorics; counting as sampling and constructing outcomes. Selection with and without replacement; permutations; counting sets vs sequences; the Unordering Principle; overcounting due to duplicates, multinomial coefficients. Lecture Slides: PDF 
Look at this summary of problemsolving strategies, most of which involve combinatorics: HTML; this is a good summary of what I will cover, although it does not explain all the formulae. The second chapter of Prob has a brief treatment of these topics as well. Bayes' Rule is covered well in Prob pp.9091, including a nice explanation in terms of trees. The form of Bayes' Rule in Prob p.90 is very general; we will discuss only the simple case P(BA). Prob p. 9 and MCS 14.9 discuss the inclusionexclusion principle. Prob discusses random sampling briefly on p.38. You should also read this link on Permutations with Repetitions;

Practice problems from Prob (not to hand in): 4.22, 4.25 (Bayes), 2.2, 2.8, 2.10


6  Th 9/20  Combinations; applications to finite probability problems; poker probabilities.
Lecture Slides: PDF 
Much of this should be review from CS 131! Prob, Ch. 2; MCS Sections 14.1  14.7 is a rather more advanced treatment of the same materal. Combinations are covered in the previous list of readings; the Wiki article section on 5card poker is very good;

Practice problems from Prob (not to hand in): 2.15, 2.16, 2.17, 2.19, 2.20, 2.12, 2.24, 2.25 HW 3: IPYNB Solution: PDF 

M 9/24 
Lab 3: Poker Probabilities  verifying the formulae by simulation: IPYNB Solution: PDF 

7  T 9/25  Counting continued: the power set and counting subsets; using combinations to count partitions; ordered partitions vs. unordered partitions; overcounting due to duplicates among subsets. Applications to probability problems.
Lecture Slides: PDF 
MCS 14.5 concerns powersets and counting subsets; here is a nice explanation about how to count partitions, with intuitive examples. 
Practice problems from Prob (not to hand in): 2.26, 2.28, 2.29, 2.72, 2.73 

8  Th 9/27  Discrete Random Variables; Probability Distributions, Functions and expressions of RVs; Expected value
Lecture Slides: PDF 
Read Prob 5.1  5.3  Practice problems from Prob (not to hand in): 5.1  5.5 HW 04: IPYNB HW Solution: PDF 

M 10/1  Lab 4: Generating Random Variates IPYNB
Solution: PDF 

9  T 10/2  Expected Value, and fair games; Variance, and Standard Deviation of RVs; Lecture Slides: PDF 
Practice problems from Prob (not to hand in): 5.8, 5.9, 5.15, 5.18, 5.20, 5.19, 5.21, 5.23 


10  Th 10/4  Important Discrete Distributions: Uniform, Bernoulli, Binomial; Geometric Lecture Slides: PDF 
Read Prob 5.4  5.5, 5.8 In Prob the Bernoulli and Binomial are explained in greater depth on pp.17780, and the Geometric on p.195. Here is a summary of some of the most useful discrete distributions: IPYNB(you do not need to know any that we do not study in lecture). For an illustration of the Binomial, take a look at this Quincunx animation: HTML 
Practice problems on Binomial from Prob (not to hand in): 6.2, 6.3, 6.5, 6.8, 6.12, 6.15 HW 05: IPYNB HW Solution: PDF 

T 10/9  Monday schedule: Labs will be held but no lecture!  Lab 5: Generating Random Variates II; Comparing Distributions
IPYNB
Solution: PDF 

11  Th 10/11  Discrete Distributions concluded: Geometric; Memoryless property of Geometric; Poisson Processes and Poisson Distribution; relationship between Poisson and Binomial. Lecture Slides: PDF 
On Poisson Distribution: Prob section 6.7. 
Reading on the Poisson Processes: HTML Practice problems on Geometric: Example 6.18 on p. 195, plus 6.46 and 6.87. Practice problems on Poisson from Prob: 6.39, 6.40, and 6.81. HW 06: IPYNBSolution: PDF 

M 10/15  Lab 6  Queueing Simulation with Discrete Distributions: IPYNB Solution: PDF 

12  T 10/16  General (continuous) Random Variables; Uniform Distribution; Importance of CDF, Introduction to Normal Distribution Lecture Slides: PDF 
Prob: 5.10, 5.11, 6.8 Brief tutorial on integration: PDF

Practice problems on continuous distributions from Prob: 5.12, 5.37


13  Th 10/18  Normal Distribution continued; Exponential distribution; Memoryless property of Exponential Distribution; Relationship between the Exponential and Poisson Distribution.
Lecture Slides: PDF 
Prob: 6.3, 6.4, & 6.5 
Practice problems on Normal from Prob: (use calculator rather than converting to Z scores with damn table!) 6.28, 6.29 , 6.21, 6.22, 6.33, 6.34 Practice problems on Exponential from from Prob: 6.89, plus look at Examples 6.19 and 6.20 on p.198. No homework this week, study for the midterm! 

M 10/22  No Lab


14  T 10/23  Review Session for Midterm  Sample Midterms: Soon!  
15  Th 10/25  Midterm Exam Midterm A Solution: PDF Midterm B Solution: PDF 
Exam will have 6 problems, and you must eliminate one, completing the other five.
Material covered will be up through lecture 12, but you are not responsible for the Normal or Exponential
Distributions (will do those on final exam); however, continuous distributions as in problem 9 on HW 6 are fair game.
There will be no questions about the labs or requiring you to write code. For questions with complicated
calculations, you may just give the appropriate formula.
Most problems will have multiple parts. One question will be literally from the list of practice problems from Schaum's on this page up through lecture 12 (but nothing about the normal or exponential), perhaps modified in some simple way so they can be done in the test environment. The rest will be similar (but not identical) to homework problems, again modified to make them doable in a test environment. I will post some additional problems from Schaums (maybe a dozen, not more) by Saturday midday, as well as some past midterms and solutions. These practice exams are just for you to see the format and so on; paying too much attention to those problems is not a good idea, because those exact problems won't appear! Focus on the Schaum's practice problems and the homeworks. Solutions to homeworks 1  5 are on this page; solution to hw 06 will be posted by Sunday night. No books, no calculators, but you may bring a single 3x5 card or a piece of paper of the same dimensions. You may typeset it but no magnifying glasses :). 
Midterm Examples with Solutions: DIR
HW 07: IPYNB Solution: PDF 

M 10/29  Lab 7: Discrete Event Simulation  Queueing with Scheduling: IPYNB
PreLab Video Lecture: YT Lab 07 with Diagrams (what you should be aiming for): PDF Solution: PDF 

16  T 10/30  Normal approximation to the Binomial; the Continuity Correction. Central Limit Theorem Lecture Slides: PDF Notebook on CLT: IPYNB Notebook on CLT PDF 
The CLT is stated on p.189 of Prob. Not much discussion. Here is a reasonable tutorial, with videos: HTML 

17  Th 11/1  Statistics as Applications of the CLT. Sampling theory and point estimation when population variance is known. Confidence Intervals. Lecture Slides: PDF 
Read Prob, Appendix A1  A4 (up to p.251) Here is a very precise and readable summary of all the major points about sampling, confidence intervals, and hypothesis testing: PDF 
HW 08: IPYNB Solution: PDF 

M 11/5  Lab 8  Stats Lab 1: ZIP Here is documentation on the scipy.norm statistics library: HTML Solution: PDF 

18  T 11/6  Hypothesis Testing
Lecture Slides: PDF 
On Hypothesis Testing, here is a nice summary of the major points, with a video lecture: HTML  
19  Th 11/8  Hypothesis testing concluded: Onetailed vs Twotailed tests; Sampling when the population parameters are unknown; Small samples and the TDistribution. Lecture Slides: PDF 
HW 09: IPYNB Solution: PDF 

M 11/12  Lab 9  Display of Multivariate Data: IPYNB
What you are aiming for: PDF Solution: PDF 

20  T 11/13  Joint Random Variables (discrete and continuous); Independence of JRVs; Conditional Random Variables  Read Schaum's 5.6  5.7, but correct the bad typo in the definition of correlation at the bottom of page 130: ρ(X,Y) = cov(X,Y) / (σ_{X}σ_{Y}) Here is my spreadsheet from lecture: XLS 

21  Th 11/15  Covariance and correlation of Joint Random Variables  HW 10: IPYNB HW 10 Solution: PDF 

M 11/19  Lab 10  Correlation and Autocorrelation: ZIP Solution: PDF 

22  T 11/20  Continuous JRVs; Least Squares and Linear Regression 
For continuous joint random variables, this is a reasonable introduction to the main points: HTML For regression: Read Prob, Appendix A.6, and I will follow fairly closely the treatment in sections 1.1  1.6 in this link. 


Thanksgiving Recess  
M 11/26  No Lab!  
23  T 11/27  Linear Models  
24  Th 11/29  Linear Models concluded; Multiple Linear Regression  I will follow closely the treatment in sections 5.1, 5.2, and 5.3 in this link 
HW 11: IPYNB
Solution: PDF 

M 12/3  
25  T 12/4  Logistic Regression Lecture Slides: PDF 
Video 1 (simpler, first of series of 5) Video 2 (more detailed) Nice summary of Logistic Regression: HTML 

26  Th 12/6  Logistic Regression Concluded Lecture Slides: PDF 

M 12/10  
27  T 12/11  Conclusions; Review for Final Exam; Course Evaluations  
M 12/17  
T 12/18  Final Exam: 12:30  2:30pm
Solution for Exam A: PDF Solution for Exam B: PDF 
Summary of Advice for Final Exam:

Table for standard normal distribution (will be provided on exam): PDF
Directory of past exams and solutions: DIR 