Syllabus

Prerequisite: Probability Theory. The topics to be covered are as follows:

1. Descriptive Statistics
   • Classification and tabulation of data, graphical representation
   • Measures of central tendency: mean, median, mode
   • Measures of dispersion: range, variance, standard deviation, coefficient of variation
   • Correlation coefficient
2. Sampling Distributions
   • Chi-square, \(t\), and \(F\) distributions
   • Central limit theorem
3. Statistical Inference
   • Point estimation, properties of point estimators: unbiasedness, consistency, efficiency, sufficiency
   • Method of moments and maximum likelihood estimation
   • Confidence interval estimation
4. Hypothesis Testing
   • Null and alternative hypotheses, Type I and Type II errors, power of a test, \(p\)-values
   • One-sample tests for mean, variance, and proportion
   • Two-sample tests, test for independence, chi-square goodness-of-fit test
5. Regression and Correlation
   • Karl Pearson's correlation, rank correlation
   • Simple linear regression and multiple regression
6. Demonstration Using R

Textbooks

• Ross, Sheldon M. Introduction to Probability and Statistics for Engineers and Scientists. Fourth edition. Academic Press/Elsevier, New Delhi, 2009. [IITJ Library]
• Hogg, Robert V.; McKean, Joseph W.; Craig, Allen T. Introduction to Mathematical Statistics. Sixth edition. Dorling Kindersley India Pvt. Ltd., New Delhi, 2005. [IITJ Library]

Reference Books

• Casella, George; Berger, Roger L. Statistical Inference. Second edition. Cengage Learning India Pvt. Ltd., New Delhi, 2002. [IITJ Library]
• Rohatgi, Vijay K.; Saleh, A. K. Md. Ehsanes. An Introduction to Probability and Statistics. Second edition. Wiley India, New Delhi, 2001. [IITJ Library]

Online Course Material

• Srinivasan, G. Introduction to Probability and Statistics. NPTEL Course Material, Department of Mathematics, IIT Madras, 2026. [NPTEL]

Evaluation

To be announced.