Undergraduate Statistics Books

If you are a beginner at Statistics, these books will give you either a very comprehensive outlook of the subject, or will be referred to very frequently in the community. If you are deciding whether to take up Statistics as an academic degree, these books may also help you gauge the conventional scope and interests of the discipline of Statistics.

0. Preliminaries

In case you want to take a look at Statistics texts for the higher-secondary-school level, here are some suggestions. Note that a higher-secondary reading of Statistics is surely beneficial but not at all mandatory for undergraduate studies.

• Introduction to Statistics -- P. K. Giri, J. Banerjee. Introduction to Statistics - Google Books
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• A West Bengal higher secondary staple.
• Deals with combinatorial probability, mathematical statistics, applied statistics, and even dabbles with a bit of number theory!
• Better to go for print options.

1. Classics and Summarizers

These books are either great summary texts in Statistics, or are frequently referred to. Their purpose is to provide a detailed overview, yet not to discourse in great depth about any singular subdiscipline of Statistics.

• Fundamentals of Statistics (Vol. 1, 2) -- A. M. Gun, M. K. Gupta, B. Dasgupta. 2015.137863.fundamentals of Statistics Vol 1 | PDF, Fundamentals Of Statistics Vol. 2 : Goon, A. M. Internet Archive
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• An Indian staple, followed in almost every college (at least in West Bengal).
• Vol. 1 deals with mathematical statistics and probability mostly, whereas Vol. 2 deals with applied statistics.
• The typesetting, the language, and the notational choices can be a little brain-wrecking at times.
• Better to go for print options, as these books are quite cheap but badly digitized.
• A First Course in Probability -- Sheldon M. Ross. A-First-Course-in-Probability.pdf
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• A question-bank and staple reading for classical (combinatorial) probability, probability axioms and definitions, probability distributions, and large number laws.
• Deals little with pure statistics if we disregard the theory of random variables.
• Fundamentals of Mathematical Statistics -- S. C. Gupta, V. K. Kapoor. 2.-B.C.A.-Elements-of-Statistics-Study-Material.pdf
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• Deals with mathematical statistics, elementary probability theory, probability distributions, and inference.
• Similar to Fundamentals of Statistics (Vol. 1, 2) -- A. M. Gun, M. K. Gupta, B. Dasgupta but with better print, better notational convention, and clearer language.
• Comprehensive in solved examples and chapter-end problems.

• Statistical Inference -- George Casella, Robert L. Berger. Statistical Inference
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• An international staple that serves a Statistician throughout his career.
• Deals with lesser combinatorial probability, carries a hint of axiomatic probability theory, provides a brief introdution to random variables, but majorly delves into actual mathematical statistics and statistical inference.
• This is not meant to be a one-read book, but instead a book meant to keep coming back to. Do not expect to understand this book at the first read like some other elementary texts.

2. Introductory Topic-specific

I will add content here in the future.

ISI MStat Interview 2024 Questions

The questions posted here were contributed by various members of the MStat 2024-2026 batch, and are not necessarily interview questions, but certainly interview-oriented. Special thanks to Rinika Jana (LinkedIn) for compiling everyone's inputs.

It is very important to remember that the interview questions are intended to probe the depth of one's understanding, and are often asked based on one's topic preferences. It is not compulsory nor expected to be able to flawlessly answer every single question below. But being proficient in at least 2-3 topics will help.

Inference

1. Given $X \sim \Bin(n,p)$, $Y \sim \Bin(m,p)$. The ultimate goal is to find what $X | X+Y$ follows. Here are some milestones --
• What does $X+Y$ follow?  Ans: $\Bin(m+n, p)$.
• Is this always true? Do we need something more?  Ans: Independence of $X$ and $Y$.
• Once the pmf is obtained for the distribution of $X|X+Y$, why is the pmf obtained independent of parameter $p$?
• Give a real life example of the need of testing
  $H_0: p=p'$ vs $H_1: p>p'$.
• Using samples $X_1,\dots,X_n \sim \Ber(p)$ and $Y_1,\dots,Y_m \sim \Ber(p')$ and the expression of the pmf you have derived, suggest a test statistic to conduct the above test.
• Why are you choosing this statistic?
• What is the critical region and why?

ISI MStat Interview

Some pointers about the nature of the interview, associated preparation, and, most importantly, the logistics -- the journey and the stay -- for the ISI MStat D-day.

The canteen and 'Old Hostel', ISI Delhi

The ISI MStat Interview is a matter of huge concern (not unnecessarily) for any MStat candidate. In this article, I give some pointers describing the nature of the interview, associated preparation, and, most importantly, the logistics -- the journey and the stay -- of the MStat interview.

1. Interview format

1. Timespan: 30-40 minutes
• Depends on how panelists like your answers, how much they want to probe your understanding of a topic, and your natural speed of figuring out hints and formulating solutions.
• Length of the interview does not at all convey success in the interview, so don't compare it with others.
2. Timing: 1 particular day (out of generally 3-4 days overall), and in any one of the 3 shifts -- morning (10 am), noon (12 pm) or afternoon (2 pm).
• In every shift, panelists try to accommodate 4-5 interviewees, so if you are the last candidate in a shift, it may drag on to the next.
• The last afternoon interview has, historically, continued as far as till 6:30 pm.
3. Location: ISI Delhi classrooms.
• You may be seated in the ISID auditorium and then called to arrive at the classroom at your turn.