Probability, Statistics and Stochastic Processes, JanuaryMay 2018
When Tuesday 12, Thursday 1112, Friday 1011; (Monday 89 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, Chebyshevâ€™s inequality, Markov inequality, Conditional expectations, Standard discrete and continuous distributions (Binomial, Poisson, Geometric, Exponential, Normal, Chisquare), 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, Studentâ€™s tdistribution, 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)
 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
 Introductory Probability and Statistical Applications, by Paul L. Meyer
Grading
Evaluation 
QuizI 
QuizII 
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.