Statistics — Syllabus & Chapters

The complete syllabus for Statistics — every chapter you need to study, and how the exam paper is structured.

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

How many chapters are there in Statistics?

The Statistics syllabus has 12 chapters, listed in full above. Cover the high-weightage chapters first using the exam pattern as a guide.

How do I know which Statistics chapters carry the most marks?

Compare the chapter list above with the exam pattern and the last few years of question papers — the topics that appear most often and the units with the highest marks are where to focus first. Always confirm weightage against the official syllabus for your exam year.

Has the Statistics syllabus changed this year?

Boards occasionally revise the syllabus or remove topics for a session. Always download the official syllabus for your exact exam year from the official GATE portal rather than relying on an older copy or a social-media list.

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.