Probability and Statistics (2023)

Convener(s)
Name: Dr. Nabin Kumar Jana Dr. Arijit Chakrabarty
Mailing Address: Reader-F
School of Mathematical Sciences
National Institute of Science Education and Research, Bhubaneswar, P.O. Jatni, Khurda, Odisha, 752050

Associate Professor
Theoretical Statistics and Mathematics Unit Indian Statistical Institute,
203 B.T. Road, Kolkata 700108
Email: nabinjana at gmail.com arijit.isi at gmail.com

Under choice based credit system, UGC made it compulsory to teach ‘Probability and Statistics’ for each Mathematics (Honours) students. Since most of the university curriculum does not have probability and statistics, college teachers are not competent enough to teach that course properly. Our school will try to bridge that gap, by exposing the college teachers with the experts of these fields to enlighten their viewpoint of these subjects while teaching.

Dates: 

Monday, July 10, 2023 - 19:00 to Friday, July 21, 2023 - 19:00

Venue: 

Venue Address: 

National Institute of Science Education and Research Bhubaneswar
P.O. Jatni, Khurda 752050, Odisha, India

Venue State: 

Venue City: 

PIN: 

752050

Syllabus: 

Syllabus:

Sr. Name of the speaker and Affiliation
 Topic of lectures Number of lectures
1

B V Rao

CMI, Chennai

 Probability I: Random experiment, probability space, finite sample spaces. Conditional probability, Bayes theorem, independence.

Real random variables (discrete and continuous), cumulative distribution function, probability mass/density functions, mathematical expectation, moments, moment generating function, characteristic function. Discrete distributions : uniform, binomial, Poisson, geometric, negative binomial, Continuous distributions : uniform, normal, exponential.

 12 lectures
2

Mousumi Bose

ISI, Kolkata

 Statistics I: Sampling and Sampling Distributions : Populations and Samples, Random Sample, distribution of the sample, Simple random sampling with and without replacement. Sample characteristics.

Sampling Distributions : Statictic, Sample moments. Sample variance, Sampling from the normal distributions, Chi-square, t and F-distributions

Estimation of parameters : Point estimation. Interval Estimation- Confidence Intervals for mean and variance of Normal Population. Mean-squared error. Properties of good estimators - unbiasedness, consistency, sufficiency, Minimum-Variance Unbiased Estimator (MVUE).

Method of Maximum likelihood : likelihood function, ML estimators for discrete and continuous models.

 12 lectures
3

Alok Goswami

Indian Association for the Cultivation of Science, Kolkata

Probability II: Joint cumulative distribution function and its properties, joint probability density functions, marginal and conditional distributions, expectation of function of two random variables, moments, covariance, correlation coefficient, independent random variables, joint moment generating function (jmgf) and calculation of covariance from jmgf, characteristic function. Conditional expectations, linear regression for two variables, regression curves. Bivariate normal distribution.

Markov and Chebyshev’s inequality, Convergence in Probability, statement and interpretation of weak law of large numbers and strong law of large numbers. Central limit theorem for independent and identically distributed random variables with finite variance.

 12 lectures
4

Arnab Chakraborty

ISI, Kolkata

Statistics II: Statistical hypothesis : Simple and composite hypotheses, null hypotheses, alternative hypotheses, one- sided and two-sided hypotheses. The critical region and test statistic, type I error and type II error, level of significance. Power function of a test, most powerful test. The p-value (observed level of significance), Calculating p-values.

Simple hypothesis versus simple alternative : Neyman-Pearson lemma (Statement only). Bivariate frequency Distribution : Bivariate data, Scatter diagram, Correlation, Linear Regression, principle of least squares and fitting of polynomials and exponential curves.

 12 lectures

References:

  1. William Feller, An introduction to Probability Theory and its Application, Volume 1, 3e.
  2. Robert V. Hogg, Joseph W. McKean and Allen T. Craig, Introduction to Mathematical Statistics, Pearson Education, Asia, 2007.
  3. Irwin Miller and Marylees Miller, John E. Freund, Mathematical Statistics with Applications, 7th Ed., Pearson Education, Asia, 2006.
  4. Sheldon Ross, Introduction to Probability Models, 9th Ed., Academic Press, Indian Reprint, 2007.
  5. Alexander M. Mood, Franklin A. Graybill and Duane C. Boes, Introduction to the Theory of Statistics, 3rd Ed., Tata McGraw- Hill, Reprint 2007

 

Time Table: 

Day Date

Lecture
1 & 2

9.00
to
11.00

 Tea11.05
to
11.25

Tutorial

11.30
to
12.30

 Lunch
12.30
to
2.25

Lecture
3 & 4

2.30
to
4.30

Tea

4.35
to
4.55

Tutorial

5.00
to
6.00

  6.05
to
6.30
    name of the speaker   name of the speaker
+
tutors		   name of the speaker    name of the speaker
+
tutors		  
Mon W
e
e
k

1

 BVR   BVR & MB   MB   MB & BVR S
n
a
c
k
s
Tues BVR   BVR & MB   MB   MB & BVR
Wed BVR   BVR & MB   MB   MB & BVR
Thu BVR   BVR & MB   MB   MB & BVR
Fri BVR   BVR & MB   MB   MB & BVR
Sat BVR   BVR & MB   MB   MB & BVR
SUNDAY : OFF
Mon W
e
e
k

2

 AG   AG & AC   AC   AC & AG S
n
a
c
k
s
Tues AG   AG & AC   AC   AC & AG
Wed AG   AG & AC   AC   AC & AG
Thu AG   AG & AC   AC   AC & AG
Fri AG   AG & AC   AC   AC & AG
Sat AG   AG & AC   AC   AC & AG

 

  • BVR: B V Rao
  • AG: Alok Goswami
  • MB: Mousumi Bose
  • AC: Arnab Chakrabort

Selected Applicants: 

 

Sr.n SID Full Name Gender Affiliation Position in College/ University University/ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
1 48247 Dr. Rakesh Ranjan Male DST-CIMS, Banaras Hindu university, Varanasi Asst. Professor Banaras Hindu University 2012 13/06/2017
2 48341 Mr. Vishalsingh Sarjeetsingh Chauhan Male Deogiri Institute of Engineering and Management Studies,
Station Road, Aurangabad- 431005		 Asst Prof University of Pune 2007  
3 48361 Dr. Ravinder Katta Male Indian Institute of Information Technology Design and Manufacturing Kurnool Assistant Professor UNIVERSITY OF HYDERABAD 2010 20/03/2017
4 48457 Ms Rutuja Sachin Kulkarni Female PES Modern College of Engineering, Pune Assistant Professor Shivaji University, Kolhapur 2020  
5 48506 Dr. Tanveer Ahmad Tarray Male Islamic university of Science and Technology, Assistant Professor University of Kashmir 2009 27/01/2016
6 48655 Dr. N Paramaguru Male Govt. Arts College for Women, Krishnagiri, Tamil Nadu Assistant Professor Annamalai University   11/09/2014
7 48856 Dr. Vikash Siwach Male Chaudhary Charan Singh Haryana Agricultural University Asst. Prof. M.D.U. Rohtak 2009 03/11/2015
8 48881 Dr Mahadev Ota Male B S Abdur Rahman Crescent Institute of Science & Technology Assistant Professor University of Madras 2009  
9 48882 Dr. Chinmay Kumar Giri Male National Institute of Science and Technology, Berhampur Asst. Prof. National Institute of Technology Rourkela 2013 01/12/2018
10 49005 Mr Saravanakumar Dhanabal Male MSS Wakf Board College Madurai Assistant Professor Madurai Kamaraj University 2006  
11 49124 Mr Pankaj Kumar Male Shiv Nadar University, India Assistant Professor Moscow Institute of Physics and Technology 2016 21/03/2023
12 49146 Dr. Sudhananda Maharana Male NIST (Autonomous) Assistant Professor Berhampur University 2012 06/11/2017
13 49184 Dr Ashis Kumar Pati Male ITER Soa Asst Prof IISER Kolkata 2014 20/06/2022
14 49199 Mr. Sagar Chakraborty Male Maulana Abul Kalam Azad University of Technology Visiting Faculty University of Kalyani 2015  
15 49261 Dr. Rajasekar S P Male Government Arts College for Women Assistant Professor Pondicherry University 2004 30/09/2020
16 49310 Mr Soumen Roy Male KREA UNIVERSITY TEACHING FELLOW IIT MADRAS CHENNAI 2013  
17 49398 Ms. Riddhi Sudhir Bharani Female Vivekanand Education society's College of Arts, Science and Commerce (Autonomous) Asst. Prof. Indian Institute of Technology Bombay 2010  
18 49671 Dr. Vikas Kumar Sharma Male Banaras Hindu University Asst. Prof. CCSU Campus Meerut 2010 05/01/2016
19 49732 Dr. Om Prakash Keshri Male Mizoram University, Aizawl Guest Faculty Indian School of Mines, Dhanbad 2012 10/09/2020
20 49838 Mr. Gaurav Tyagi Male Mahamana Malviya College Assistant Professor M.Sc. 2009  
21 50151 Prof. Suman Kalyan Ghosh Male Alliance School of Applied Mathematics, Alliance University Assistant Professor IIT Kanpur 2006  
22 50172 Mr. Amit Roy Male NISER Bhubaneswar Postdoctoral fellow Chennai Mathematical Institute 2015 01/03/2021
  Waiting list      
1 48512 Mr. Subrata Golui Male Indian Institute of Technology Guwahati PhD Indian Institute of Engineering Science and Technology (IIEST), Shibpur, (M.Sc) 2016 21/04/2023
2 49869 Mr. Muzammil Khan Male Maulana Azad National Institute of Technology Bhopal Research Scholar Bundelkhand University Jhansi 2018  
3 49886 Mr. Sumangal Bhattacharya Male Indian Institute of Technology Tirupati PhD Indian Institute of Engineering Science and Technology Shibpur 2016  
4 50255 Ms. Srijita Mondal Female Jadavpur University PhD IIT Kharagpur 2016  

 

 

How to Reach: 

Click the following link for more information: https://www.niser.ac.in/content/how-reach

 

School Short Name: 

ps

Last Date Application: 

Sunday, May 28, 2023

School Type: 

IST

Separate faculty form: 

0