Introduction to Probability Theory, Statistics and Stochastic Processes

4 Credits (3-1-0)

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, Addison-Wesley, 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.

 



Tutorial Sheets

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


Tutorial Sheet 2 Answer


Tutorial Sheet 3 Answer


Tutorial Sheet 4 Answer


Tutorial Sheet 5 Answer


Tutorial Sheet 6 Answer


Tutorial Sheet 7 Answer


Tutorial Sheet 8 Answer


Tutorial Sheet 9 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

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Students can join the discussion forum in

https://www.facebook.com/Probability-Statistics-and-Stochastic-Processes-Course-123219464954505/http://web.iitd.ac.in/%7Edharmar/mal250/fblogo.jpg

 

See Course Website: http://web.iitd.ac.in/~dharmar/IITJ/main.htm for further details.

 

 

 

 

(S Dharmaraja)

COURSE COORDINATOR