Introduction to Probability Theory, Statistics and
Stochastic Processes
4 Credits (310)
I Semester 2017 18
INFORMATION SHEET
Probability Theory: Probability Theory: Axioms of probability, Probability space, Random variable, Some common discrete and continuous distributions, Two and higher dimensional distributions, Functions of random variables, Conditional distributions, Covariance, correlation coefficient, Law of large numbers, Central limit theorem.
(No. of Lectures  14)
Statistics: Sampling Distribution, Parameter Estimation, Maximum Likelihood Estimator Confidence Interval, Hypothesis Testing, Goodness of Fit test.
(No. of Lectures  14)
Stochastic Processes: Definition of Stochastic process, Classification and properties of stochastic processes, Simple stochastic processes, Stationary processes, Discrete and continuous time Markov chains, Classification of states, Limiting distribution, Birth and death process, Poisson process, Steady state and transient distributions, Simple Markovian queuing models (M/M/1, M/M/1/N, M/M/c/N, M/M/N/N, M/M/∞).
(No. of Lectures  14)
Main Text Books
1. Introduction to
Probability and Stochastic Processes with Applications, Liliana Blanco
Castaneda, Viswanathan Arunachalam,
S Dharmaraja, Wiley, 2012.
2. Probability and
Statistics with Reliability, Queueing and Computer Science Applications, Kishor S. Trivedi, John Wiley, second edition, 2001.
3. Introduction to
Probability Models, Sheldon M. Ross, Academic Press, tenth edition, 2009.
4.
Introduction to
probability and statistics for engineers and scientists, Sheldon M. Ross,
Elsevier, fourth edition, 2012.
Reference Books
1.
Introductory Probability and Statistical
Applications, Paul L. Meyer, AddisonWesley, 1966.
2.
Stochastic Processes, J. Medhi,
New Age International Publishers, 3rd edition, 2009.
3.
Stochastic Processes, Video course, NPTEL Phase II.
4.
An Introduction to Probability Theory and its
Applications, Vol. I & II, William Feller, Wiley Eastern, third edition,
2000.
Note: It seems, some students found that the answers provided for few problems in the following tutorial sheets are not correct. Please let me know these errors by email.
Tutorial Sheet 1 Answer
Scheme of Evaluation
Two Minor Tests of 25 Marks each 
2X 25 
50 
One Major Examination 
1 X 50 
50 

Total 
100 
IMPORTANT INFORMATION
·
Students are encouraged to contact the Course
Coordinator or Tutorial Teachers for any difficulties regarding the course.
·
Only those students who could not appear for
one of the minor tests due to medical reasons are eligible for the make up examination which will be conducted before the major examination. However, submission of a valid medical
certificate adhering to the institute norms is mandatory.
·
The evaluated minor answer books will be returned to the students and
they must retain with them as a proof of the marks secured.
INFORMATION about the Instructors
Name 
Room No. 
Phone No. 
Email 
S Dharmaraja 
MZ 164 
7104 
dharmar@maths.iitd.ac.in 
INFORMATION about the Tutorial Teachers
Name 
Room No. 
Phone No. 
Email 
 
 
 
 
Students
can join the discussion forum in
https://www.facebook.com/ProbabilityStatisticsandStochasticProcessesCourse123219464954505/
See Course Website: http://web.iitd.ac.in/~dharmar/IITJ/main.htm
for further details.
(S Dharmaraja)
COURSE COORDINATOR