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: By appointment.

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

Other Reference Textbooks

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
Jan 15- Jan 19 Chapter 1 from BT Chapter 1 from BT Chapter 2 from BT
Jan 22- Jan 26
Jan 29- Feb 2 Chapter 2 from BT Chapter 2 from BT Chapter 3 from BT
Feb 5- Feb 9 Chapter 3 from BT Chapter 4 from BT Chapter 4 from BT
Feb 12- Feb 16 Chapter 5 from BT Chapter 5 from BT Quiz I Review
Feb 19- Feb 23 Quiz I Chapter 8 from M\(^2\) Chapter 8 from M\(^2\) Chapter 8 from M\(^2\)
Feb 26- Mar 2 Chapter 10 from M\(^2\) Chapter 10 from M\(^2\) Chapter 10 from M\(^2\)
Mar 5- Mar 9 Chapter 11 from M\(^2\) Chapter 11 from M\(^2\) Chapter 11 from M\(^2\)
Mar 12- Mar 16 Chapter 12 from M\(^2\) Chapter 12 from M\(^2\) Chapter 12 from M\(^2\)
Mar 19- Mar 23 Chapter 13 from M\(^2\) Chapter 13 from M\(^2\) Chapter 13 from M\(^2\)
Mar 26- Mar 30 Chapter 8 from Ibe Quiz II Review
Apr 2- Apr 6 Quiz II Chapter 8 from Ibe Chapter 8 from Ibe Chapter 8 from Ibe
Apr 9- Apr 13 Chapter 10 from Ibe Chapter 10 from Ibe Chapter 10 from Ibe
Apr 16- Apr 20 Chapter 10 from Ibe Chapter 10 from Ibe Chapter 10 from Ibe
Apr 23- Apr 27 Backup Class/Review Backup Class/Review End Sem Review
Apr 30- May 4 End Sem

More details will be added later.