Probability, Statistics and Stochastic Processes, JanuaryMay 2019
When Tuesday 12, Thursday 1112, Friday 1011; (Monday 89 will be used as a reserve slot)
Where Class Room Complex 305
Instructor
Sivaram Ambikasaran,
Office: NAC 648
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
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 
QuizI 
QuizII 
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.
All the chapters are from BT unless indicated explicitly.
From the book, we will be omitting Chapter 8 and Sections 5.3, 5.5 and 7.5.
Week 
Monday 
Tuesday 
Thursday 
Friday 
Practice problems 
Jan 14 Jan 18 





Jan 21 Jan 25 



Finish Chapter 1 

Jan 28 Feb 1 





Feb 4 Feb 8 



Finish Chapter 2 

Feb 11 Feb 15 



Finish Till Section 3.2 

Feb 18 Feb 22 
QUIZI 


Finish Chapter 3 

Feb 25 Mar 1 





Mar 4 Mar 8 



Finish Chapter 4 

Mar 11 Mar 15 



Finish Chapter 5 

Mar 18 Mar 22 



Finish Till Section 9.1 

Mar 25 Mar 29 
QUIZII 




Apr 1 Apr 5 



Finish Chapter 9 

Apr 8 Apr 12 



Finish Chapter 6 

Apr 15 Apr 19 



Holiday 

Apr 22 Apr 26 



Finish Chapter 7 

Apr 29 May 3 
END SEM 




More details will be added later.