Statistics

This is a complete, free study companion for Statistics — built around what the exam actually asks. The topics examiners repeat most are Valid CDF/PMF/PDF and normalizing constant, Expectation, variance, and moments from a given distribution, and Marginal and conditional distributions from joint density. The syllabus runs to 12 chapters. Below you'll find the full topic-frequency ranking, the exam paper pattern, every chapter, a step-by-step study plan, and the official downloads — everything in one place.

Everything here is free. We're an independent student resource, not the official GATE body, so always confirm the current syllabus and exam dates on the official GATE website before you rely on them.

Key information

Level: ST
Programme: Statistics
Exam: GATE Statistics Exam (ST)
Conducted by: IISc and IIT

Most frequently examined topics

#	Topic	Times asked
1	Valid CDF/PMF/PDF and normalizing constant	7
2	Expectation, variance, and moments from a given distribution	7
3	Marginal and conditional distributions from joint density	7
4	Chi-square, t, and F sampling distributions	7
5	Maximum likelihood estimator and invariance	7
6	Size, power, level, and p-value of tests	7
7	Least squares estimation in regression	7
8	Conditional probability	6
9	Independence of events	6
10	Distribution of functions of random variables	6
11	Normal distribution standardization and probabilities	6
12	Independence of random variables	6

Counted across the official previous-year question papers we have analysed for this subject. It shows what has been asked before — it does not predict what will appear in your exam. Always confirm the current syllabus on the official portal.

What you will study (chapters)

Chapter 1: Probability Axioms, conditional probability, Bayes' theorem, independence
Chapter 2: Random Variables and Distributions: distribution function, pmf/pdf, moments, MGF, quantiles, functions of RVs
Chapter 3: Standard discrete and continuous univariate distributions (Bernoulli, Binomial, Geometric, Negative Binomial, Hypergeometric, Uniform, Exponential, Gamma, Beta, Weibull, Normal)
Chapter 4: Jointly distributed random variables and sampling distributions: order statistics, multinomial, bivariate normal; sampling distributions (central chi-square, t, F)
Chapter 5: Convergence in distribution, convergence in probability, convergence almost surely; LLN; CLT; Delta method; Slutsky; Borel-Cantelli
Chapter 6: Stochastic Processes: Markov chains; Poisson process; birth-death process; Brownian motion
Chapter 7: Estimation: Sufficiency, minimal sufficiency, factorization theorem, completeness; exponential families; unbiased estimation; Rao-Blackwell; Lehmann-Scheffe; Cramer-Rao; Consistent
Chapter 8: Interval Estimation: Confidence intervals; pivotal quantities; coverage probability
Chapter 9: Hypothesis Testing: Neyman-Pearson lemma; most powerful tests; likelihood ratio tests; MLR property; uniformly most powerful tests; large-sample tests
Chapter 10: Non-parametric Statistics: Empirical distribution function; GOF tests; Chi-square; Kolmogorov-Smirnov; Sign test; Wilcoxon; Mann-Whitney; rank correlations
Chapter 11: Multivariate Analysis: Multivariate normal distribution; MLE for mean vector and dispersion; Wishart; Hotelling's T^2; correlation
Chapter 12: Regression Analysis: Simple and multiple linear regression; Gauss-Markov; R^2; distribution of quadratic forms; tests for regression coefficients; confidence intervals

How to study Statistics and score well

Start with the highest-frequency topics — In Statistics, Valid CDF/PMF/PDF and normalizing constant, Expectation, variance, and moments from a given distribution, Marginal and conditional distributions from joint density, and Chi-square, t, and F sampling distributions appear again and again in past papers. Master these first — they return the most marks for the time you put in.
Practise with previous-year papers — Solve the last 5–10 years of GATE Statistics papers under timed, exam-like conditions. Past papers show exactly which topics repeat and how questions are worded.
Revise actively, not passively — Write a one-page summary for each of the 12 chapters — key definitions, formulas and the points examiners reward — then re-test yourself instead of re-reading.
Mark your answers with the official scheme — After each practice paper, score yourself against the official marking scheme. It shows how marks are awarded step-by-step, so you learn to present answers the way examiners expect.

Exam tips: how to score higher in Statistics

Where students lose marks: attempting questions they have not truly eliminated options for, spending too long on one hard question, and rushing the sections they know best. Read the whole paper first, bank the marks you are sure of, and come back to the rest.

Manage your time and guess carefully: split your time in proportion to the marks each section carries and keep a few minutes at the end to check. This paper carries negative marking, so attempt a question only when you can rule out at least one or two options — a blind guess costs you marks. Confirm the exact marking scheme for your session on the official portal.

Frequently asked questions

What are the most important topics in Statistics?

Based on past papers, the most frequently asked topics include Valid CDF/PMF/PDF and normalizing constant, Expectation, variance, and moments from a given distribution, Marginal and conditional distributions from joint density. The full ranked list with how often each appears is in the "Most important topics" section above.

Where can I download Statistics previous-year question papers?

Official GATE previous-year question papers are available on the official GATE website. Open the Question Papers section for the direct link, plus the exam pattern and the topics that repeat most.

How can I prepare for Statistics faster?

Start with the highest-frequency topics, learn the exam pattern so you know how each section is marked, and practise with past papers. A subject-aware study tutor can quiz you on exactly these topics.

A Gyani AI tutor trained on the Statistics syllabus and past papers can quiz you on the most-asked topics and show you exactly what to revise.