Probability, Statistics and Stochastic Processes, January-May 2018

When Tuesday 1-2, Thursday 11-12, Friday 10-11; (Monday 8-9 will be used as a reserve slot)
Where Class Room Complex 304

Instructor

Sivaram Ambikasaran,

Office: HSB 241C
Office hours: 9:30 AM to 11:30 AM, Mondays.

Those who sit in the class by Sivaram Ambikasaran in CRC 304, fill in the details here

Syllabus

Probability Axiomatic definition of probability, Independent Events, Baye's theorem, Discrete and continuous random variables, Distribution, Functions of random variables, Expectation, Variance, Correlation coefficient, Chebyshev’s inequality, Markov inequality, Conditional expectations, Standard discrete and continuous distributions (Binomial, Poisson, Geometric, Exponential, Normal, Chi-square), Moment generating function, Sums of random variables, Law of large numbers, Central limit theorem, Normal approximation to Binomial.
Statistics Sampling distribution, Estimation of parameters, Maximum likelihood estimates, Confidence intervals, Student’s t-distribution, Testing hypothesis, Goodness of fit.
Stochastic Processes Continuous and discrete random process, Stationary random process, Bernoulli process, Poisson process, Markov chain.

Textbooks

Introduction to Probability, by Dimitri Bertsekas and John N. Tsitsiklis (referred as BT in Calendar)
Introductory Probability and Statistical Applications, by Paul L. Meyer (referred as PLM in Calendar)
John E. Freund's Mathematical Statistics with Applications, by Irwin Miller and Marylees Miller (referred as M\(^2\) in Calendar)
Fundamentals of Applied Probability and Random Processes, by Oliver C. Ibe (referred as Ibe in Calendar)

Other Reference Textbooks

Introduction to Probability Models, by Sheldon M. Ross

Grading

Evaluation	Quiz-I	Quiz-II	EndSem
Points	20	20	60

Quiz I will be on February \(19\), Monday.

Quiz II will be on April \(2\), Monday.

End Sem will be on May \(1\), Tuesday.

Calendar

Below is a very rough calendar, which will be updated as we progress through the course.

Week	Monday	Tuesday	Thursday	Friday	Practice problems

Jan 15- Jan 19		Chapter 1 from BT	Chapter 1 from BT	Chapter 1 from BT	Chapter \(1\) practice problems Solutions
Jan 22- Jan 26
Jan 29- Feb 2		Chapter 1 from BT	Chapter 2 from BT	Chapter 2 from BT
Feb 5- Feb 9		Chapter 2 from BT	Chapter 2 from BT	Chapter 2 from BT	Chapter \(2\) practice problems
Feb 12- Feb 16	Chapter 2,3 from BT	Chapter 3 from BT	Chapter 3 from BT	Chapter 3 from BT
Feb 19- Feb 23	Quiz I	Chapter 3.4 from BT	Chapter 3.5 from BT	Chapter 4.1 from BT
Feb 26- Mar 2		Chapter 4.2 from BT
Mar 5- Mar 9		Chapter 10 from PLM	Chapter 10 from PLM	Chapter 5 from BT/ Chapter 12 from PLM
Mar 12- Mar 16	Chapter 5 from BT/ Chapter 12 from PLM	Chapter 5 from BT/ Chapter 12 from PLM	Chapter 13 from PLM	Chapter 13 from PLM
Mar 19- Mar 23	Chapter 13 from PLM	Chapter 14 from PLM	Chapter 14 from PLM	Chapter 14 from PLM
Mar 26- Mar 30	Chapter 14 from PLM				Practice problems
Apr 2- Apr 6	Quiz II	Chapter 15 from PLM	Chapter 15 from PLM
Apr 9- Apr 13	Chapter 6.1 from BT
Apr 16- Apr 20		Chapter 6.2 from BT	Chapter 6.2 from BT	Chapter 7.1 from BT
Apr 23- Apr 27	Chapter 7.2 from BT	Chapter 7.3 from BT	Chapter 7.3 from BT	Review
Apr 30- May 4		End Sem