Probability, Statistics and Stochastic Processes, January-May 2019

When Tuesday 1-2, Thursday 11-12, Friday 10-11; (Monday 8-9 will be used as a reserve slot)
Where Class Room Complex 305

Instructor

Sivaram Ambikasaran,

Office: NAC 648

Problem Sets

Problem Set 1 Problem Set 2 Problem Set 3 Problem Set 4 Problem Set 5

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 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)

Other Reference Textbooks

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)

Grading

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

Quiz I will be on February \(18\), Monday.

Quiz II will be on March \(25\), Monday.

End Sem will be on April \(29\), Monday.

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 14- Jan 18			First class- Introduction	Chapter 1, BT
Jan 21- Jan 25	No Class	Chapter 1, BT	Chapter 1, BT	No Class
Jan 28- Feb 1	Chapter 1, BT	Chapter 1, BT	Chapter 2, BT	Chapter 2, BT
Feb 4- Feb 8	No Class	Chapter 2, BT	Chapter 2, BT	Chapter 2, BT
Feb 11- Feb 15	No Class	Chapter 3, BT	Chapter 3, BT	Chapter 3, BT
Feb 18- Feb 22	QUIZ-I	No Class	No Class	No Class
Feb 25- Mar 1	Chapter 3, BT	Chapter 3, BT	No Class	Chapter 3, BT
Mar 4- Mar 8	Chapter 4, BT	Chapter 4, BT	Chapter 4, BT	No Class
Mar 11- Mar 15	No Class	Chapter 4, 5, BT	Chapter 5, BT	Chapter 5, BT
Mar 18- Mar 22	Chapter 5, 9, BT	Section 9.1, BT		Section 9.1, BT
Mar 25- Mar 29	QUIZ-II	Section 9.1, BT	Section 9.1, BT	Hypothesis Testing, PLM
Apr 1- Apr 5		Hypothesis Testing, PLM	Hypothesis Testing, PLM	Chapter 6, BT
Apr 8- Apr 12		Chapter 6, BT	Chapter 6, BT	Finish Chapter 6, BT
Apr 15- Apr 19	Chapter 7, BT	Chapter 7, BT	Chapter 7, BT	Holiday
Apr 22- Apr 26		Chapter 7	Chapter 7	Finish Chapter 7
Apr 29- May 3	END SEM