CS 215 - Data Interpretation and Analysis Instructor: Ajit Rajwade and Suyash Awate Office: SIA-218, KReSIT Building Email: Lecture Venue:LH-101 Lecture Timings: Slot 8, Monday and Thursday 2:00 to 3:25 pm Instructor Office Hours (in room SIA-218): Tuesdays 10:30 am to 11:30 am, Friday 11:00 am to 12 pm, or after class, or by appointment via email (also feel free to send queries over email) Teaching Assistants: Ravi Mishra, Rajeev Kumar, Kalyani Dole, Pratik Kalshetti, Krishna Harsha, Siddhant Garg [Email ids: {ravimsr,rverma,kalyanid,pratikm,krishna.harsha,siddhant}@cse DOT ac DOT in ]

Topics to be covered (tentative list)

• Descriptive statistics
• Discrete and continuous probability
• Random variables and expectation
• Special random variables: Gaussian, Bernoulli, Beta, Gamma, Uniform, Poisson, Exponential, Binomial, etc.
• Hypothesis testing
• Parameter estimation
• Regression
• Probability density estimation

Intended Audience

Learning Materials and Textbooks

• Lecture slides that will be regularly posted. I may occasionally post links to applets or videos, or additional material such as problem sets.
• We will use moodle for posting assignments and grades
• Course textbook: Introduction to Probability and Statistics for Engineers and Scientists: Fourth Edition

Computational Resources

• MATLAB at IITB
(Note: this is an older version of MATLAB available at IITB. While we have much more recent versions now, this older version is sufficient for everything we will do in this course. You may try the newer version from here if the older one doesn't work.)
• Matlab tutorial 1
• Matlab tutorial 2
• Matlab tutorial 3
• The MathWorks - MATLAB Tutorial
• Matlab Primer
• On-line Matlab Help
• Writing Fast Matlab Code (pdf)
• One more tutorial for writing fast matlab code
• Code Vectorization Guide
• Matlab Programmin Style Guidelines (pdf)
• Matlab array manipulation

Grading Policy (tenative)

• Mid-sem exam: 25%
• Final exam (cumulative): 25%
• Programming and written assignments (about five): 35% - all to be done in groups of 2 students.
• Two pre-announced quizzes: 15% total

Other Policies

• Attendance is mandatory. Students with less than 80% attendance may be given a DX grade.
• Assignments will be given out (typically) once every two or three weeks. They must be submitted on or before the deadline. No late assignments will be accepted. The programming components of the assignments will typically involve MATLAB, so you must be willing to learn it quickly.
• We will adopt a zero-tolerance policy against any forms of plagiarism or any other form of cheating. Just don't do it! In cases of plagiarism, givers and takers will both be considered equally responsible.
• This course is (inherently) cumulative. The syllabus for the final exam will include everything taught during the semester.

Tutorials

• See here

Homework Solutions

Quizzes

Lecture Schedule:

Date	Content of the Lecture	Assignments/Readings/Notes
18/07 (Mon)	Introduction, course overview and course policies Descriptive statistics: key terminology Methods to represent data: frequency tables, bar/line graphs, frequency polygon, pie-chart Concept of frequency and relative frequency Cumulative frequency plots Interesting examples of histograms of intensity values in an image	Slides: Course Overview Slides: Descriptive statistics Readings: section 2.1, 2.2 from the textbook by Sheldon Ross
21/07 (Thurs)	Interesting examples of histograms of intensity values in an image Concept of mean, median, mode, percentile, standard deviation and variance with examples Mean as minimizer of total squared deviations, median as minimizer of sum of absolute deviations Chebyshev's inequality: two-sided and one-sided with examples	Slides: Descriptive statistics Readings: section 2.1 to 2.4 from the textbook by Sheldon Ross Non-calculus proof to show that the median minimizes the sum of absolute deviations
25/07 (Mon)	Proof of Chebyshev's inequality: two-sided and one-sided Correlation coefficient: centered and uncentered versions, properties and examples Correlation and causation A demo of a simple MATLAB program	Slides: Descriptive statistics Readings: Read chapter 2 from the textbook by Sheldon Ross (except section 2.5)
28/07 (Thurs)	MATLAB demo.	Please consult some of the MATLAB tutorials mentioned above on this webpage Examples covered in class: matrix and vector operations, code vectorization, functions for different types of plots and graphs, statistical functions (mean, median, variance, standard deviation)
01/08 (Mon)	Discrete probability: sample space, event, composition of events: union, intersection, complement, exclusive or, De Morgan's laws Boole's and Bonferroni's inequalities Conditional probability, Bayes rule, False Positive Paradox	Slides
04/08 (Thurs)	Random variable: concept, discrete and continuous random variables Probability mass function (pmf), cumulative distribution function (cdf) and probability density function (pdf) Expected value for discrete and continuous random variables Expected value of a function of a random variable The mean and the median as minimizers of squared and absolute losses respectively (with proofs) Variance and standard deviation, with alternate expressions Markov's and Chebyshev's inequality: with proofs	Slides Read chapter 4 of the textbook
08/08 (Mon)	Weak law of large numbers along with proof, statement of strong law of large numbers Gambler's fallacy Concept of joint PMF, PDF, CDF Concept of covariance, concept of mutual independence and pairwise independence Concept of moment generating function, two different proof of uniqueness of moment generating function for discrete random variables, properties of momenet generating functions	Slides Read chapter 4 of the textbook
11/08 (Thurs)	Concept of conditional PDF, CDF, PMF; conditional expectation and variance with examples Bernoulli, binomial and Poisson distributions and their properties: mean, variance, MGF, mode and median (in some cases)	Slides Slides (families of random variables) Read sections 5.1 and 5.2 of the textbook
18/08 (Thurs)	Gaussian distribution: mean, variance, median, mode, MGF, other properties Central limit theorem: statement of theorem, MATLAB code to demo the theorem, and one application	Slides (families of random variables) Read sections 5.5, 6.1, 6.2 of the textbook
22/08 (Mon)	Proof of central limit theorem using the MGF de Moivre Laplace theorem - stated without proof Distribution of sample mean and sample covariance - chi-square distribution and its MGF for n degrees of freedom, genesis of the chi square distribution for n = 1 Uniform distribution - mean, median, variance, MGF, application in sampling from arbitrary PMFs	Slides (families of random variables) Read sections 5.5, 6.1, 6.2, 6.4, 6.5 of the textbook
25/08 (Thu)	Exponential distribution: motivation, pdf, cdf, mean, variance, MGF, memorylessness Multinomial distribution: concept of mean vector and covariance matrix; mean, covariance and MGF of multinomial Introduction to hypergeometric distribution	Slides (families of random variables) Read chapters 5 and 6 of the textbook (skip sections 5.6.1, 5.7, 5.8.2, 5.8.3, 5.9, 6.6)
29/08 (Mon)	Concept of maximum likelihood estimation Maximum likelihood (ML) estimates for parameters of Bernoulli, Poisson, Gaussian and uniform distributions Concept of biased estimator and example (ML estimator of the variance of a Gaussian when the mean is also unknown) Introduction to the concept of the variance of an estimator	Slides Read sections 7.1, 7.2, 7.7 of the textbook
1/09 (Thu)	Bias, variance, mean squared error of an estimator, proof that mean squared error = squared bias + variance; consistency of an estimator Derivation of bias, MSE, variance for two different estimators of the parameter of a uniform distribution Concept of confidence interval - one-sided and two-sided, examples for mean of a Gaussian with known variance, variance of a Gaussian, mean of a Bernoulli (approximate)	Slides AdditionalNotes on MLE Read sections 7.1, 7.2, 7.3.1, 7.5, 7.7 of the textbook