Summer I, 2016







Lecture 
Date 
Lecture & Lab Topics 
Readings, from Bertsekas unless otherwise noted 
Homeworks and Tests 
Labs 
1  M 5/23  Administrative matters; Goals of the course; Motivating Examples: Why should a computer scientist know probability and statistics? Introduction to Classical Probability: Coin flips and random choices. Set theory and probability. 
Here is chapter one of The Drunkard's Walk (the whole thing is worth reading, but I will talk about the flight instructors example on pages 7 and 8): PDF Here is a link to an article on traffic deaths after 9/11: HTML Here is the New Yorker article on earthquakes in the Pacific Northwest: HTML Here is the wiki page explaining the "Base Rate Falacy" (look at Example 1, on breathalyzer tests): 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, in a later lecture): HTML Sections 1.1  1.2 (PDF) 

2  T 5/24  Classical Probability  Sections 1.1  1.2 (PDF)  HW 01: HTML Solution: HTML 

3  W 5/25  Classical Probability 



R 5/26  Conditional Probability  HW 02: HTML Solution: HTML 

4  T 5/31  Total Probability Theorem and Bayes' Theorem; Independence 
HW 03: HTML Solution: HTML 

5  W6/1  Counting principles and combinatorics; permutations and combinations; accounting for duplicates; permutations; applications to probability problems. 
Section 1.6 Also, look at this summary of problemsolving strategies, most of which involve combinatorics: HTML



6  R 6/2  Counting continued; multinomial coefficients  Read this link on Permutations with Repetitions;  
7  F 6/3  Random Variables; Binomial Distribution  Section 2.1 & 2.2 
HW 04: HTML Solution: HTML Here is a summary of some of the most useful discrete distributions: HTML (so far we have done only Bernoulli, Binomial, and Geometrical) Here are some useful Python functions: Distributions.py 

8  M 6/6  Important Distributions: Binomial, Geometric, Poisson 

Here are the first five chapters from Schaum's, with lots of practice problems (with solutions): 1, 2, 3, 4, 5  
9  T 6/7  First Midterm Exam  Midterm Solution: PDF  HW 05: HTML Solution: HTML 

10  W 6/8  Discrete Distributions continued: Expected values, variance, standard deviation; Joint Random Variables  Here is a spreadsheet to work with joint random variables: JointDistributions.xlsx  
11  R 6/9  JRVs: Conditional, Independence  HW 06: HTML Solutions: HTML 

12  M 6/13  Discrete JRVs concluded: Relationship of Binomial and Poisson; Covariance and correlation, expected value and variance of sums of RVs; Sampling as repeated sum of RV.  Cov & cor are in section 4.2; Expected value and variance of sum of RVs is at end of chapter 2, or you can also see a brief summary here: HTML Here is my spreadsheet from lecture: XLS 
HW 07: HTML Solution: HTML 

13  T 6/14  General (continuous) Random Variables; probabilities as areas under a curve; PDFs and CDFs.; Normal Distribution, Exponential Distribution  Chapter 3 Lecture on Normal Distribution: PDF 

W 6/15  Exponential distribution; relationship of Exponential and Geometric; relationship of Exponential and Poisson; Normal approximation to Binomial;  Chapter 3  Here is a collection of all kinds of functions related to distributions, which I was using in class today: Distributions.py  
R 6/16  Joint Continuous RVs  Chapter 3  
M 6/20  Limit Theorems; Central Limit Theorem  Chapter 4  HW 08: HTML Solution: HTML 

T 6/21  Introduction to Statistics: Sampling theory, point estimates, confidence intervals, hypothesis testing  Chapter 9.1 For a more basic introduction, consult your friendly neighborhood statistics textbook on the topics listed, or here: PDF 

W 6/22  Small sample estimation: the tdistribution;  Chapter 9.1 & 9.2  
R 6/23  Second midterm  HW 09: HTML (due next Wednesday)  
M 6/27  Linear Regression; ChiSquared test; Distribution Fitting  Chapter 9 has a good description of regression and its motivations, and on the ChiSquared Test (p.505); there are many other treatments of this material, e.g., HTML 

T 6/28  Distribution Fitting: Error margins, regression and normal plots  Here is a research paper on normal plots: PDF; the "Background and Motivation" section describes the basic idea.  
W 6/29  Review of HW 09; Course evaluations and conclusions.  
R 6/30  Final Exam 