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MAL6150: Probability and Statistics

Autumn 2026–27 (Semester I) · IIT Jodhpur
Core course for MSc (Mathematics) students in their 1st year

L-T-P (C): 3-1-0 (4)
Prerequisite: None

Syllabus

Objectives

  1. Demonstrate an understanding of the basic principles of probability theory.
  2. Use of the properties of discrete and continuous random variables with their joint, marginal, and conditional distributions.
  3. Use of the various families of probability distributions to model various types of data.

Learning outcomes

  1. Understanding of probability theory and statistics to solve industrial problems.
  2. Understanding of random sampling, theory of estimation and testing of hypotheses.

Contents

  1. Probability Spaces and Random Variables (12 lectures)
    • Probability space, conditional probability, Bayes' theorem
    • Random variable, cumulative distribution function and its properties, probability density function
    • Functions of a random variable, standard discrete and continuous distributions and their applications
    • Transformations, moments, Chebyshev's inequality
  2. Joint Distributions (8 lectures)
    • Random vectors, joint, marginal, and conditional distributions
    • Conditional expectation, independence, correlation and regression
    • Bivariate normal distribution, functions of random vectors, transformations
  3. Limit Theorems (3 lectures)
    • Convergence of sequences of random variables
    • Weak and strong laws of large numbers, central limit theorem
  4. Estimation and Tests of Hypotheses (16 lectures)
    • Sampling distributions, point estimation of parameters
    • Maximum likelihood method and method of moments
    • Interval estimation, testing of hypotheses

Textbooks

Reference Books

Online Course Material

Lectures

Classes are held in Slot H in lecture hall LH204, Lecture Hall Complex - I [Google Maps]:

Tutorials are held in lecture hall MT113, Department of Metallurgical and Materials Engineering [Google Maps]:

Office hours are held in my office, Room 116, Department of Mathematics [Google Maps]:

A calendar of lectures, tutorials, and assessment dates is maintained for this course [Google Calendar]. Sign in with your IIT Jodhpur account to view or subscribe.

Please note timetable adjustments as per the Academic Calendar.

Teaching Assistants

Evaluation

Attendance

Attendance in lectures is compulsory. If you miss lectures for valid reasons (e.g., medical), please inform the instructor promptly. Students who do not meet the 80% attendance requirement will be awarded an F grade. [Google Sheets]

Assessments

Course materials

The primary text for this course is Vijay K. Rohatgi and A. K. Md. Ehsanes Saleh, An Introduction to Probability and Statistics, second edition, Wiley India, New Delhi, 2001. [IITJ Library]