Statistics — Textbook & Study Material

Download the official textbook for Statistics and see the full chapter list so you know exactly what to cover.

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

Frequently asked questions

Is the Statistics textbook available for free?

The book linked above is free to download from its source — we link to it rather than hosting a copy, so you always get the current edition. Note that GATE itself does not publish or prescribe a textbook; it publishes the syllabus and past papers, and you should check any book against the current official syllabus.

Is the Statistics textbook enough to score well, or do I need extra notes?

No single book covers GATE. Use the official syllabus as your checklist, pick a standard reference per topic, and spend most of your time on past papers and timed practice — the exam rewards problem-solving speed far more than re-reading.

How should I study the Statistics textbook chapter by chapter?

Cover the high-weightage chapters first (use the exam pattern as a guide), make a one-page summary per chapter, and immediately solve a few past-paper questions on it. Active recall beats passive re-reading.

How can I prepare for Statistics faster?

Begin with the most-frequently-asked topics and the last few years of question papers, then test yourself under timed conditions. If you want guided help, you can use the free AI study tutor for Statistics — practise past-paper questions and get instant feedback — or a focused Statistics study guide that condenses the syllabus into the topics that matter most — both are free to start.