Fall , 2015







Lecture 
Date 
Lecture & Lab Topics 
Readings, from DeGroot unless otherwise noted 
Homeworks and Tests 
Labs 
1  R 9/3  Administrative matters; Goals of the course; Motivating Examples: Why should a computer scientist know probability and statistics?  Recommended: Chapter One from "The Drunkard's Walk": PDF Here is a link to an article on traffic deaths after 9/11, with slightly different numbers than I presented: HTML Here is the wiki page explaining the "Base Rate Falacy" (the breathalyzer example at the end of class): HTML 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, next week): HTML 

2  T 9/8  Classical Probability: Basic definitions; Set theory (e.g., Venn Diagrams) as a model for Sample Spaces and Events; Geometric Probability (uncountable sample spaces).  Sections 1.1  1.4  
3  R 9/10  Axioms and theorems of probability; Geometric Probability (uncountable sample spaces);  Section 1.5  We will cover this in detail; pay particular attention to last two pages, on uncountable sample spaces! Section 1.6  We basically covered this in class today, but review it! 
HW 01: HTML Solution: HTML 

M 9/14  Lab 01: Generating random numbers and running simulations  Lab 01: HTML Solution: TXT 

4  T 9/15  The general Inclusion/Exclusion Principle; Combinatorics and counting finite sets; Multiplication principle and tree diagrams; The Monty Hall Problem (application of the Multiplication Principle); Choosing with and without replacement; Permutations. 
Read this short article on the InclusionExclusion Principle: HTML and then read page 48 (skipping the proof if you like....) in the textbook. Sections 1.7 (main reading) Also Google "probability tree diagram" and read the first link (easy) and then read sections 14.1 and 14.2 of the following analysis of the "Monty Hall Problem": PDF 

5  R 9/17  Counting principles continued; permutations and combinations; accounting for duplicates; applications to classical probability. 
Section 1.8  HW 02: HTML Solution: HTML 

M 9/21  Lab 02: Computing with permutations and combinations; simulation continued.  Read about Pascal's Triangle and its relationship to C(N,K) here.  Lab 02: HTML Solution: TXT 

6  T 9/22  Counting concluded: combinations and subsets; accounting for repetitions; multinomial coefficients;  Section 1.8, Read this link on Permutations with Repetitions; Section 1.9 

7  R 9/24  Discrete nonequiprobably sample spaces; Histograms vs distributions; Conditional Probability  Read about Histograms here: Section 2.1 
HW03: HTML Solution: HTML 

M 9/28  Lab 03: Drawing probabilities in Python: PMFs and CDFs  Lab 03: HTML Solution: PDF 

8  T 9/29  Conditional Probability; Independence  Section 2.2  Quiz 01 at end of class;  
9  R 10/1  Bayes Theorem, Discrete Random Variables; Distributions, PMFs and CDFs  Read about Bayes Theorem here: HTML Just read the first two screenfuls or so, with the background, statement of the theorem and the example about Addison. Read chapter 3.1 up to page 98 on Discrete Random Variables. This is just a way of formalizing what we have already been doing! 
HW04: HTML Solution: HTML 

M 10/5  Lab 04: Introduction to Pandas and data analysis  Lab 04: HTML Solution: TXT 

10  T 10/6  Multiple Random Variables on same sample space; Properties of random variables: mode, expected value/mean  Our textbook spreads out the various characteristics of random variables, and I would rather you read Chapter Five from the Schaum's, which I provide since not all of you will have bought it: PDF This reading uses f(x) instead of p(x) for the PMF, but otherwise it is fairly consistent with what we have been doing. 

11  R 10/8  Properties of random variables: moments; variance and standard deviation, skewness, kurtosis. Uniform Distributions, Bernoulli Trials, Binomial Distribution 
Finish reading Schaum's on properties of random variables. Read pp. 9799 in DeGroot, or look at the StatTrek page on Binomial: HTML 
HW05: HTML Solution: HTML 

T 10/13  Monday Schedule; Lab 05  Lab 05: HTML Solution: PDF 

12  R 10/15  Characteristics of the Binomial: Mean, Mode, Variance, Standard Deviation; Binomial Experiments; Why is the binomial so important? Generalizations of the Binomial: Multinomial, Hypergeometric Distributions 
Read about Multinomial and Hypergeometric Distributions in sections 5.9 and 5.3 of the textbook; just read to get the basic idea (these are generalizations of the binomial)
OR, read pages 1934 of the Schaum's Outline (easier) here: PDF 
HW06: HTML Solution: HTML 

M 10/19  Lab 06: Fitting distributions to data; Generating random variates by simulation.  Lab 06: HTML Solution: PDF 

13  T 10/20  Other discrete distributions: Poisson  Read about Poisson in Section 5.4 of the textbook; this whole section is very good, but you should skip all the proofs, and skip Theorems 5.4.3 and 5.4.4. The Wiki page on the Poisson is also good: HTML, read up through the Properties section for mean, variance, & mode. 
Quiz 02 Solution: PDF  
14  R 10/22  Conclusions on discrete distributions: Poisson concluded; the Geometric distribution; the Negative Binomial distribution. Continuous random variables: Uniform distribution, why CDFs are important; integrals in place of summations 
Read about the Negative Binomial and the Geometric in 5.5; we will use the formula at the top of p.298 for the PMF; skip Theorems 5.5.2 and 5.5.3 but look carefully at Theorem 5.5.5 (the Memoryless Property of Geometric). You can also look at these in the summary of distributions which I have linked at the top of the page.

HW07: HTML Solution: HTML


M 10/26  Lab 07: Generating random variates by the inverse method; approximating the Binomial with the Poisson  Lab 07: HTML Solution: PDF 

15  T 10/27  Continuous random variables: Uniform distribution, why CDFs are important; integrals in place of summations Normal Distribution 
Remind yourself about the properties of continuous distributions by looking through section 3.2. The wiki page on continuous distributions is also useful: HTML If you forget how integrals work, you might want to glance over the Wiki article: HTML Read pp.302303 on the motivation and definition of the Normal Distribution (Def 5.6.1), and look at Definition 5.6.2 on the Standard Normal Distribution. The Wiki page on the normal distribution is excellent: HTML 
PPT Lecture on Normal Distribution: PDF 

16  R 10/29  Approximating the binomial with the Normal distribution; Exponential Distribution; relationship between Exponential and Poisson.  Read about the normal approximation to the binomial here: HTML On Exponential: Read pp.3214; also see the Wiki Page: HTML up through "Memoryless Property" and also read "Occurrences of Events" 
HW08: HTML Solution: HTML 

M 11/2  No Lab!  
T 11/3  Conclusions on Distributions; Theoretical results about distributions: Cheveshev's Inequality; Law of Large Numbers; Central Limit Theorem 


17  R 11/5  Midterm  Midterm Solution: PDF  
M 11/9  No lab! 


18  T 11/10  Joint random variables; Independent RVs  Please look at the section "Discrete Joint Distributions" in 3.4 and then read 3.5 on Marginal Distributions. As usual, the Wiki article on this is very good: https://en.wikipedia.org/wiki/Joint_probability_distribution 

19  R 11/12  Covariance, Correlation, Autocorrelation  Read section 4.6 in the textbook (again, skipping all the proofs, and understanding that we are only really considering the discrete case) The Schaum's Outline has a brief treatment of these topics starting on page 129 here: PDF And, again, the Wiki article is useful: HTML

HW09: HTML Solution: HTML 

M 11/16  Lab 08: Computing Covariance and Correlation; Correlation in data sets  Lab 08: HTML Solution: TXT 

20  T 11/17  Regression and Curve Fitting  The Schaum's treatment of these topics in Appendix A6, starting on p.257, is fairly good: PDF The Wiki article on "Simple Linear Regression" is also good: HTML


21  R 11/19  Guest Lecture by Steve Homer: Probabilistic Algorithms 


M 11/23  Lab 09: Displaying Joint Distributions  Lab 09: HTML Solution: TXT 

22  T 11/24  Statistics: Sampling Theory and overview  
23  R 11/26  No Class: Thanksgiving Break 


M 11/30  Lab 10: Topic TBD  Lab 10: HTML Solution: TXT 

23  T 12/1  Statistics: Statistical Inference  
24  R 12/3  Statistics: Statistical Inference  HW12: HTML Solution: HTML 

M 12/7  Lab 11: Topic TBD  Final Project: HTML 

25  T 12/8  Statistics: Statistical Inference  
26  R 12/10  Statistics: Statistical Inference; Wrapup and comments on final exam 


Final Project due  
R 12/17  Final Exam 12:30  2:30pm 