Shalabh
shalab@iitk.ac.in
shalabh1@yahoo.com
Department of Mathematics & Statistics
Indian
MSO201A : Probability and Statistics
Instructor-in-Charge:
Dr. Shalabh
Office: FB511, E-mail:
shalab@iitk.ac.in
Syllabus:
Algebra of Sets: sets and classes, limit of a sequence of sets, fields, sigma-fields, and their elementary properties
Probability: Classical, relative frequency and axiomatic definitions of probability, addition rule and conditional probability, multiplication rule, theorem of total probability, Bayes' Theorem and independence of events
Random Variables and Distributions: Discrete, continuous and mixed random variables, probability mass, probability density and cumulative distribution functions, mathematical expectation, moments, probability and moment generating function, median and quantiles, Markov inequality, Chebyshev's inequality.
Special Distributions: Discrete uniform, binomial, geometric, negative binomial, hypergeometric, Poisson, continuous uniform, exponential, gamma, Weibull, beta, normal, Cauchy, double exponential distributions
Reliability Theory: reliability and hazard rate, reliability of series and parallel systems
Functions of random variables and their distributions
Joint Distributions: Joint, marginal and conditional distributions, product moments, correlation and regression, independence of random variables, bivariate normal distribution
Transformations: functions of random vectors, distributions of order statistics, distributions of sums of random variables
Sampling Distributions: Distributions of the sample mean and the sample variance for a normal population, Chi-Square, t and F distributions. Weak Law of Large Numbers and Central Limit Theorems.
Descriptive Statistics: Graphical representation, measures of locations and variability
Estimation: Unbiasedness, consistency, the method of moments and the method of maximum likelihood estimation, confidence intervals for parameters in one sample and two sample problems of normal populations, confidence intervals for proportions
Testing of Hypotheses: Null and alternative hypotheses, the critical and acceptance regions, two types of error, power of the test, the most powerful test and Neyman-Pearson Fundamental Lemma, tests for one sample and two sample problems for normal populations, tests for proportions, Chi-square goodness of fit test and its applications
Text Book: Introduction to Mathematical Statistics (Seventh Edition)
Authors: Robert V. Hogg, J.W. McKean, and and Allen T. Craig
Publisher: Pearson Education, Asia (Low price edition)
Course Timings:
Lectures- Mon, Wed, Fri : 10:00 AM - 12:00 P.M. : Location: L2
Tutorials- Thu : 10:00 AM - 12:00 P.M.: Location: L2, L3, L4, L5
Academic Performance Evaluation Scheme:
Quiz- 20%, Mid Semester Examination- 30%, End Semester Examination- 50%
Tutorial Sections:
|
Section No. |
Tutor |
Location |
List of Students (in pdf) |
|
1 |
Jisha Francis (E-mail: jisha@iitk.ac.in) |
L2 |
Section
1 |
|
2 |
Deepak Prajapati (E-mail: deepakdp@iitk.ac.in) |
L3 |
Section
2 |
|
3 |
Shuvashree Mondal (E-mail: shuvasri@iitk.ac.in) |
L4 |
Section
3 |
|
4 |
Chitraipa Chakraborty (E-mail: chitrac@iitk.ac.in) |
L5 |
Section
4 |
Announcements:
Seating Plan: ERES : All sections in L20
Seating Plan: ERES : All sections in L20
Quiz Announcements:
Quiz 2 will be on 30 June 2017 at 10 AM-10:30 AM in L7.
The assignments will be discussed during tutorial classes.