IITM BS Probability and Statistics (MA3101): Syllabus and Tips

Probability and Statistics (MA3101) is a 4 credit department elective at the degree level of the IITM BS Electronic Systems programme. It covers the basics of probability, discrete and continuous random variables, the law of large numbers and the central limit theorem, and three ways to estimate unknown values. The handbook lists no prerequisite. The syllabus states its aim simply: probability and statistics for electronic systems.

The Sep 2025 syllabus and the ES handbook agree on the code, credits and level. The handbook's main course table puts it in the semester 7 block. The syllabus does not name an instructor.

This is an ES course. It is not the same as the statistics courses in the Data Science programme.

What you learn in Probability and Statistics

The syllabus has 4 modules with no week plan. The second module is long, so it is split in two below.

1. Module 1: the rules of probability. Experiments, outcomes, sample spaces and events. The axioms of probability and the addition rule. Conditional probability, the multiplication rule, total probability, Bayes' theorem and independence.
2. Module 2, first half: discrete random variables. Bernoulli trials and the binomial, geometric and Poisson distributions. PMFs, and joint, marginal and conditional PMFs for more than one variable. Functions of random variables, expected value, mean and variance, correlation and covariance.
3. Module 2, second half: continuous random variables. Moving from discrete to continuous, CDFs, densities and common distributions. Functions of a continuous variable and their expectations. Joint, marginal and conditional densities, independence, and histograms.
4. Modules 3 and 4: from samples to estimates. Independent samples, sample statistics and the empirical distribution. Sums of independent variables, the law of large numbers and the central limit theorem. Finally, estimation: MMSE estimators, Bayesian estimators and maximum likelihood estimators.

The textbooks are "Probability and Statistics" by DeGroot and Schervish (4th edition) and "A Modern Introduction to Probability and Statistics" by Dekking, Kraaikamp, Lopuhaa and Meester. The reference is "Probability and Random Processes" by Grimmett and Stirzaker.

How the course is assessed

The syllabus does not describe grading. The handbook's general pattern for ES courses is weekly online assignments, two in-person quizzes and an in-person end term exam, with details in each course's grading document. No lab is paired with this course.

Where it counts

It is one of 8 courses on the ES department elective list. You take 5 of them, worth 20 credits, for the BS degree. It is not part of any ES minor. See the full list in ES degree level courses.

If you plan the Machine Learning minor, starting with Machine Learning Foundations, this course gives you the probability those topics lean on. It does not count toward that minor itself.

Who finds it hard and how to prepare

If your last probability class was in Class 12, the first module will feel familiar, and then the course speeds up. Continuous random variables need integration, including double integrals for joint densities. Estimation in Module 4 is the most abstract part.

• Revise integration from your maths courses, especially integrating over a region for joint densities.
• Solve a few problems every day rather than many before a quiz. Probability improves with steady practice.
• Check your answers by simulation. Toss a virtual coin 10,000 times in Python and see the law of large numbers happen. Python Programming (CS1002) from the diploma is enough for this.
• For each distribution, write down its PMF or density, mean, variance and one real example from electronics, such as noise or random bit errors.

What to take before and after

Before: Math for Electronics II and the earlier maths courses. After: the machine learning open electives, which lean on probability and estimation.

Common questions

Is MA3101 compulsory for ES students?

No. It is a department elective. You pick 5 from the list of 8, so you can skip it.

Can a Data Science statistics course replace MA3101?

The ES handbook does not list any DS statistics course as a replacement. None of the DS open electives it lists is a statistics course.

How much coding is in this course?

The syllabus does not mention coding or any software. Even so, simulating problems in Python is a good way to check your answers.