IITM BS Statistics for Data Science II (BSMA1004): Syllabus and Tips

Statistics for Data Science II (BSMA1004), or Stats 2, is a 4 credit foundation course. It moves from one random variable to many, then to estimating unknown values from data and testing hypotheses. You need Statistics 1 (BSMA1002) first. Maths 2 (BSMA1003) is a corequisite, so take it before Stats 2 or in the same term.

The instructor is Prof. Andrew Thangaraj of the Electrical Engineering Department, IIT Madras.

Course page and handbook differ slightly

The handbook lists only Statistics 1 as the prerequisite, with Maths 2 as the corequisite. The course page also lists Maths 1 (BSMA1001). In practice this changes nothing. Maths 2 needs Maths 1, so anyone allowed to take Maths 2 has already passed Maths 1.

What you learn

• Weeks 1 to 3: many discrete random variables. Joint distributions, independence, functions of random variables, expected value, variance, covariance, correlation and inequalities. The page uses casino games as an example for expectation.
• Weeks 4 and 5: continuous random variables. Density functions and expectations, two continuous variables at once, averages and limit theorems, and jointly Gaussian variables. You also build probability models from real data, such as height and weight data and IPL powerplay data, with a Colab demo.
• Week 6: refresher week. A pause to consolidate before the second half.
• Weeks 7 to 9: estimation. Two weeks on estimation and inference, then a week on Bayesian estimation.
• Weeks 10 to 12: hypothesis testing. Two weeks of hypothesis testing, then a revision week.

The page's outcome list also mentions interval estimation, tests about a mean and a variance, and simple regression models with related tests.

How it is assessed

The course page lists 12 weeks of coursework, weekly online assignments, 2 in-person invigilated quizzes and 1 in-person invigilated end term exam. There is no OPPE.

Where it counts

• Foundation level. It is one of the 8 foundation courses. All 8 must be done before any diploma level course.
• Direct entry. If you enter the Data Science diploma through the direct entry qualifier, the handbook says you start with Maths 2 and Stats 2.
• Later courses. Machine Learning Foundations ends with probabilistic models, the exponential family and parameter estimation. At the degree level, Linear Statistical Models opens with a review of estimation and hypothesis testing.

Who finds it hard and how to prepare

Statistics 1 feels like working with data and counting. Stats 2 leans on calculus. Continuous variables need integration, and joint distributions need double sums or double integrals. If your Maths 1 calculus was shaky, or you take Maths 2 in the same term with little free time, weeks 4 and 5 can feel heavy. The second half is about clear reasoning: what the estimator is, and what exactly you are testing.

• Revise integration before the term. Maths 1 covered it. You will use it every week from week 4.
• Draw before you calculate. For a joint distribution, draw the table or the region first. Wrong limits are an easy slip, and a quick sketch catches them.
• Use week 6 for real work. Redo the assignment questions you got wrong in weeks 1 to 5.
• Write every test the same way. State the null hypothesis, the alternative, the test statistic and the decision rule, in that order, every time.
• Use the course volumes. The page offers two downloads, one on joint discrete and one on joint continuous distributions. The suggested book is Probability and Statistics with Examples using R by Athreya, Sarkar and Tanner.

For a wider plan across both statistics courses, read how to improve your IITM BS statistics scores.

What to take before and after

• Before: Statistics 1 and Maths 1.
• With or before: Maths 2. Taking both in one term is allowed, but plan your hours.
• After: the Diploma in Data Science courses. Machine Learning Foundations and Machine Learning Techniques both come back to estimation, including maximum likelihood and Bayesian estimation.

Common questions

Can I take Stats 2 without Maths 2?

No. Maths 2 is a corequisite. You must take it before Stats 2 or in the same term. The handbook says you cannot do Stats 2 without having done Maths 2.

Do I need to learn R for Stats 2?

The page does not list R as a requirement. The suggested book uses R and week 5 uses a Colab demo. Your grading document and assignments will show what you need.

What happens in the refresher and revision weeks?

The page lists week 6 as a refresher week and week 12 as a revision week, with no new topics named. Use them to catch up and to practise old questions.