How to crack/clear IIT JAM Mathematical Statistics exam

This post is a part of series of articles that I am writing about IIT JAM MS exam. In an earlier post, I wrote about "How I got AIR 16 in JAM MS 2020" and I am now going to go into more detail about how one should ideally prepare for IIT JAM Mathematical Statistics exam.

Whatever I tell in this article is how I think one should prepare ideally for the exam and not actually how I prepared for the exam. I tried following the sources of lectures that I am going to mention here but due to laziness and time constraints, I couldn't fully complete the lectures or exercises. But nonetheless, with lots of practice and a good understanding of the basics, I managed to score good mark and secure a comfortable rank.

It is best to explain the strategy for cracking the exam topic wise, so I am going to start by listing out the sources for each topic in syllabus and how to cover them.

The Mathematical Statistics (MS) test paper comprises Mathematics (40% weightage) and Statistics (60% weightage).

Mathematics

1) Sequences and Series:

I found this topic to be the toughest among all the topics in the syllabus and had a really hard time covering it. My suggestion would be to cover the basics in detail initially from any one of the usually recommended books like Bartle and Sherbert. I also studied from Real Analysis by SK Mapa and found it really helpful.

Since, I couldn’t solve the previous year questions from this topic easily, so I had to spend a lot of time here and also practice a lot of questions. I would also suggest to practice the derivations 1 or 2 times if you have sufficient time for the preparation because Real Analysis is such a topic that needs intuition and that is only going to come after studying a lot of it. Since the amount of good questions that can come in exams are available in limited quantity only so practicing proofs is a good way to boost self- confidence.

For practicing problems, I would suggest practicing examples and exercises from both the books that I have mentioned above and from a book called Problems in Mathematical Analysis-1. This book is just about Problems and it has lots of questions on Sequence and Series. There are lots of questions that are out of syllabus and way too tough so practice selectively. Solutions to problems are available at the end of the book.

One can also try exercises from books on Calculus by George Thomas and Howard, Anton, Davis. These books have easy to medium questions on sequence and series and can help in boosting self-confidence.

To sum up, just practice as much as you can from these books, and it will be sufficient for the exam.

2) Differential Calculus:

In this topic, Limits, Continuity and Differentiability are the easy portions and can be understood without much difficulty. After some practice, one will become proficient in these areas.

The tough portions are all the sub-topics that come after these portions. My strategy here was again to cover basic and the practice as many questions as I can. Since this topic has a lot in common with JEE syllabus so I practiced from my FIITJEE package on Differential Calculus and from a book by Cengage on Differential Calculus. The Cengage book was really helpful as it had lots of examples, questions along with solutions and also good theory too. So, I would definitely suggest everyone to practice for this area from that book. It will be more than sufficient.

3) Integral Calculus:

This topic is easier than the rest but has some tricky portions such as Volume. Questions on solving just the integral are easy and not that difficult as one would encounter in JEE. Here the focus is mostly on the application side and on topics like arc length, areas and Volumes.

For understanding the theory behind formulas for Arc Length and Volume, I referred to youtube videos by Professor Leonard . And I practiced from these books

George Thomas Calculus,

Howard Anton Davis Calculus,

James Stewart Early Transcendental.

These books are more than enough for practicing for questions on Integral Calculus which is a relatively easier topic.

4) Matrices:

Linear Algebra is a very important topic which is crucial from an application point of view since it is used everywhere in areas of Statistics which deal with Multiple Variables. So, a thorough understanding of Linear Algebra is more important than just covering it from an exam point of view.

Therefore, I would suggest to complete the course by Gilbert Strang on Linear Algebra available on mit.ocw.edu. You may not finish the whole course but only those portions that are common with the syllabus if you don’t have much time. I would also recommend to complete the assignments or the exercises from his book for this course . Although they are more practical based but they will really help in cementing your understanding and thinking intuitively about Matrices.

This will definitely take up time so do this only if you have sufficient time available to devote to Linear Algebra.

Besides this, I would suggest practicing from the book by Samvedna Publications on Linear Algebra. The book is not that good but it has a lot of examples and questions which are really helpful so I will suggest you to buy it. Another book that I used was Higher Algebra by SK Mapa. I had not purchased this book for the exam but for a different reason. Nonetheless, I found it to be good and you may buy it if you can get a second hand copy of it or get it xeroxed from somewhere.

Statistics

5) Probability:

This section has a lot of basic topics and the questions that come related to basic probability are very similar to those that come in JEE Main or Advanced so I specially practiced from the FIITJEE package for Probability and the Previous Years Questions of JEE. One can also do the back exercise of Probability chapter from FMS and that will be good enough too.

6) Rest of the topics in Statistics-

Unlike the above-mentioned topics, I don’t have detailed info for each of the rest of the topics in Statistics because I didn’t find them to be hard apart from Inference. But that doesn’t mean I didn’t practice rest of the topics sufficiently. I just can’t suggest books for each of the topics but I will suggest some books that cover all these topics and I practiced all these topics from these books. The books are-

Statistical Inference by Casella,Berger ( For Inference only)

An Introduction to Probability and Statistics by Rohatgi , Saleh (For all topics)

Introduction to Theory of Statistics by Mood,Graybill (All topics)

FMS, SC Gupta (All topics)

Introducing Probability and Statistics by Bansi Lal (Everything apart from Inference)

These books are more than enough for practicing almost all the topics in Statistics. Only, Inference is one topic that is tough and has limited amount of good questions available for practice. For that I used to practice my notes from college repeatedly and from all these books. And that was enough for the exam. Even though out of the 5 questions I left in the exam, 2-3 were from Inference but I think I did good enough.

If you have no prior knowledge of Probability and are looking for lectures then I will suggest you to start with Stat 110 by Harvard University. The lectures are excellent and assignments are great too. They will really help in improving your concepts and think intuitively about the subject.

So. this is the overall strategy for covering the whole syllabus. It took me 6 months to cover the syllabus and additional 4 months to practice and improve my weak areas. I spent 2 more months practicing previous year papers and reviewing everything. Then it was time for exam. So, overall it took me exactly 1 year to prepare for the exam but I believe with more hard work, one can do it in a shorter time period.

One more thing that I would like to share is that my approach in all the topics was to understand the basics of a topic and try attempting questions simultaneously while studying that topic. As soon as a topic was finished, I used to start solving previous year questions from that topic. If I could solve them without any issues then I wouldn’t practice more questions and stop. Else, if I would find that I am having some problems in solving questions then I would try to analyze the problems and understand the issues that I am facing while solving questions. After this, I would go back to a recommended book for the topic and try to go deeper in the theory, understand it in a better way and solve more questions on it. I would then repeat the whole cycle again and again until I felt that I good enough in that topic. This does not mean that I was excellent in all the topics but it meant that I was good in enough in almost all and great in few which allowed me to attempt all the easy and medium questions in the exam.

The last thing I would like to share is that my approach toward the paper was very exam based that focused more on practicing the questions rather than spending time with theory. This will not work in case of ISI exam since it requires a different level of conceptual understanding and more practice. So, this is the drawback of this approach and one should be mindful of it.

I hope the two articles that I wrote about JAM preparation were helpful to you. If you still have questions about JAM preparation then feel free to ask in the comment section or contact me through mail and I will try to help you out as soon as possible.

PS- Almost all the book that are mentioned here are available in my drive folder. So you don’t need to buy them all.

UPDATE 1- Someone asked me to share my formula sheets so I am sharing the links to those here. Since my handwriting is bad so it won’t be possible to use the sheets directly but one can copy the formulas and create a formula sheet by themselves. It will take some time but it’s totally worth the effort and almost a necessary task for cracking JAM.

Differential Calculus Linear Algebra 1

Linear Algebra 2

Linear Algebra 3

Sequence and Series -1

Sequence and Series- 2 Probability Theory

Random Variables and Distribution Function

Discrete Distribution

Continuous Distributions Sampling Distribution Joint Distribution

Statistical Inference

UPDATE 2- I have finally managed to get hold of pdf copies of notes for all the topics covered in JAM MS. But those notes aren’t mine and therefore I can’t share those publicly here, however if someone needs to look at the notes then he or she may contact me personally and I will share the link to the folder containing those notes.