IIT JAM Mathematical Statistics Syllabus 2026

The syllabus is published in the JAM information brochure. In brief:

Mathematics

• Sequences and series, differential and integral calculus, functions of several variables
• Matrices, determinants, eigenvalues and eigenvectors

Probability

• Axioms of probability, conditional probability, Bayes' theorem, independence
• Random variables, expectation, moments and moment generating functions, Chebyshev's inequality

Distributions

• Binomial, Poisson, geometric, uniform, exponential, gamma, normal and chi-square distributions
• Joint, marginal and conditional distributions, covariance and correlation, order statistics, limit theorems

Statistics

• Sampling distributions, point estimation: unbiasedness, MLE, Cramér–Rao bound
• Interval estimation and testing of hypotheses: error types, power, chi-square tests

• Probability: conditional probability and Bayes' theorem, independence, Chebyshev's inequality
• Random variables: expectation, variance, moments and moment generating functions, covariance and correlation
• Distributions: binomial, Poisson, geometric, uniform, exponential, gamma, normal and chi-square, with their means and variances
• Inference: unbiased estimators, maximum likelihood, Cramér–Rao bound, confidence intervals, Type I and II errors, power, chi-square tests
• Mathematics base: limits, series, integrals, matrices, determinants and eigenvalues

1. Weeks 1–2: calculus, series and matrices as the base.
2. Weeks 3–5: probability and random variables, deriving each moment yourself.
3. Weeks 6–8: standard distributions, joint distributions and order statistics.
4. Weeks 9–10: estimation and testing, then timed full mocks and previous-year JAM questions.