IIT JAM Mathematical Statistics Syllabus 2026, All Topics & Official PDF

The IIT JAM 2026 is scheduled to be conducted on February 15, 2026 in a Computer-Based Test (CBT) mode for admission to postgraduate courses offered by IITs, NITs and some other prestigious institutions. Candidates aspiring to pursue a master’s programme in Mathematical Statistics through JAM 2026 must plan their exam preparation strategy according to the IIT JAM 2026 Mathematical Statistics, as the exam question paper will consist of 60 questions carrying 100 marks based on the syllabus. This SciAstra article provides all the important details about the syllabus to help candidates with their exam preparation. It covers important topics and subtopics for the IIT JAM Mathematical Statistics paper, along with access to the official syllabus PDF.

JAM Exam Pattern 2026

Candidates preparing for IIT JAM 2026 must know the pattern of the exam, as it provides an overview of the question paper. This helps candidates align their preparation with the IIT JAM 2026 question paper. Check out a brief description of the IIT JAM 2026 exam question paper below:

Section	Question Type	Details	Question Numbers
Section A	Multiple Choice Questions (MCQ)	Only one correct option out of four choices	Q.1 – Q.10, Q.11 – Q.30
Section B	Multiple Select Questions (MSQ)	One or more correct choices	Q.31 – Q.40
Section C	Numerical Answer Type (NAT)	Real number entered via virtual keyboard, no choices provided	Q.41 – Q.50, Q.51 – Q.60

IIT JAM 2026 Marking Scheme:

Section	Marks per Question	Number of Questions	Total Marks	Marking Scheme
Section A	1 (Q.1 – Q.10)  2 (Q.11 – Q.30)	10 20	10 40	Negative marking: -1/3 mark for 1-mark questions, -2/3 mark for 2-mark questions
Section B	2	10	20	No negative or partial marking
Section C	1 (Q.41 – Q.50) 2 (Q.51 – Q.60)	10 10	10 20	No negative marking

• Total Questions: 60
• Total Marks: 100

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IIT JAM 2026 Mathematical Statistics Syllabus

The IIT JAM 2026 question paper for Mathematical Statistics will contain three sections: Section A (Multiple Choice Questions), Section B (Multiple Select Questions), and Section C (Numerical Answer Type – NAT). The questions will be based on the following topics from the IIT JAM Mathematical Statistics syllabus 2026 given below:

Section	Topics	Areas Covered / Subtopics
Section 1	Sequences and Series of real numbers	Sequences of real numbers, convergence and limits, Cauchy sequences, monotonic sequences, limits of standard sequences, limit superior and inferior, infinite series (convergence/divergence), convergence of series with non-negative terms, comparison test, limit comparison test, D’Alembert’s ratio test, Cauchy’s n-th root test, Cauchy’s condensation test, integral test, absolute convergence, Leibnitz’s test for alternating series, conditional convergence, power series and radius of convergence.
Section 2	Differential Calculus of one and two real variables, and Integral Calculus	Differential Calculus (one variable): Limits, continuity, differentiability, properties of continuous/differentiable functions, Rolle’s theorem, Lagrange’s mean value theorem, higher-order derivatives, Leibniz’s rule, Taylor’s theorem (Lagrange’s and Cauchy’s form), Taylor/Maclaurin series, indeterminate forms, L’Hospital’s rule, maxima and minima (local/global), points of inflection.  Differential Calculus (two variables): Limits, continuity, differentiability, partial/total differentiation, successive differentiation, maxima/minima, Hessian matrix, saddle points, constrained optimisation (Lagrange multiplier). Integral Calculus: Fundamental theorems, Leibniz’s rule, differentiation under integral sign, improper integrals, Beta and Gamma integrals, double integrals, change of order, transformation of variables, and applications (arc lengths, areas, and volumes).
Section 3	Matrices and Determinants	Vector spaces (ℝn and ℂn), span, linear dependence/independence, dimension, basis, null space, algebra of matrices, symmetric/skew-symmetric, Hermitian/skew-Hermitian, orthogonal/unitary, idempotent/nilpotent matrices, determinants (properties, applications, transformations), determinant of product, singular/non-singular matrices, trace, adjoint, inverse, rank and nullity, row-rank, column-rank, rank theorems, row reduction, echelon forms, systems of equations (consistent/inconsistent), Cramer’s rule, characteristic roots and vectors, Cayley-Hamilton theorem, quadratic forms, definiteness of matrices (positive, negative, semi-definite).
Section 4	Descriptive Statistics and Probability	Descriptive Statistics: Concepts of sample and population, types of data, tabular/graphical representation, measures of central tendency (mean, median, mode, etc.), measures of dispersion (range, variance, SD, etc.), moments, skewness, kurtosis, bivariate data, covariance, correlations (simple, partial, multiple), and Spearman’s rank correlation.  Probability: Random experiments, sample space, event algebra, definitions of probability (relative frequency/axiomatic), properties, addition theorem, geometric probability, Boole’s and Bonferroni’s inequalities, conditional probability, multiplication rule, total probability theorem, Bayes’ theorem, independence of events.
Section 5	Univariate Distributions	Random variables, cumulative distribution function (cdf), discrete/continuous variables, pmf, pdf, distribution of functions (Jacobian method), expectation and moments, mean, median, mode, variance, coefficient of variation, quantiles, skewness, kurtosis, moment generating function (mgf), inequalities (Markov, Chebyshev). Distributions: Degenerate, Bernoulli, Binomial, Negative binomial, Geometric, Poisson, Hypergeometric, Uniform, Exponential, Double exponential, Gamma, Beta (I & II), Normal, Cauchy.
Section 6	Multivariate Distributions	Random vectors, joint/marginal cdfs, pmfs, pdfs, conditional cdfs, conditional distributions, independence of random variables, transformations (Jacobian), expectations of functions of random vectors, joint moments, covariance, correlation, joint MGFs, conditional moments/expectations, additive properties (Binomial, Poisson, Gamma, Normal), multinomial distribution, and bivariate normal distribution (marginal/conditional distributions, properties).
Section 7	Limit Theorems	Convergence (in probability, mean square, almost sure, in distribution), inter-relations of convergences, weak law of large numbers, strong law of large numbers, and central limit theorem (i.i.d., finite variance).
Section 8	Sampling Distributions	Random sample, parameter, statistic, sampling distribution, order statistics, distributions of smallest/largest order statistics (discrete/continuous), Chi-square distribution (definition, pdf derivation, properties, additive property, limiting form), t-distribution (definition, pdf derivation, properties, limiting form), and F-distribution (definition, pdf derivation, properties, reciprocal distribution, relationships between t, F, χ²).
Section 9	Estimation	Properties of estimators: unbiasedness, sufficiency, consistency, relative efficiency, complete statistic, UMVUE, Rao-Blackwell theorem, Lehmann-Scheffe theorem, and Cramer-Rao inequality. Methods: method of moments, maximum likelihood estimation, invariance, least squares estimation (linear regression). Confidence intervals for normal, two-normal, and exponential distributions.
Section 10	Testing of Hypotheses	Null/alternative hypotheses, type I & II errors, critical region, significance level, size, power, p-value, most powerful/UMP tests, Neyman-Pearson lemma, and likelihood ratio tests (univariate normal distribution).
Section 11	Nonparametric Methods	Tests of randomness (runs test), empirical distribution function, Kolmogorov-Smirnov test (one sample), sign tests (one/two samples), Mann-Whitney test.
Section 12	Stochastic Processes	Discrete-time Markov chain: transition probability matrix, higher-order transitions, Chapman-Kolmogorov equation, classification of states/chains, stationary and limiting distributions. Poisson process: properties, interarrival and waiting times.

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IIT JAM 2026 Mathematical Statistics Syllabus PDF

IIT Bombay has provided the IIT JAM 2026 official syllabus for Mathematical Statistics subjects on the JAM website – jam2026.iitb.ac.in. The PDF for the same official syllabus is also available below: 

IIT JAM 2026 Mathematical Statistics Syllabus PDF (Official)

IIT JAM 2026 Mathematics Syllabus

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Best Books for IIT JAM Mathematical Statistics Preparation

The best books for preparing for the IIT JAM 2026 Mathematical Statistics paper are those that cover questions, topics, and concepts based on the IIT JAM Mathematical Statistics syllabus. Another important criterion to select these books is to ensure that the books are written or published by renowned and credible authors or publishers. Check out the best books for IIT JAM Mathematical Statistics listed below:

Book	Author / Publisher
Fundamentals of Mathematical Statistics	S. C. Gupta & V. K. Kapoor
An Introduction to Probability & Statistics	V. K. Rohatgi
Introduction to the Theory of Statistics	Mood & Graybill
Introduction to Mathematical Statistics	Robert V. Hogg & Craig McKean Hogg
IIT-JAM: MSc Mathematical Statistics (15 Years Solved Papers)	Anand Kumar
Complete Resource Manual MSc Mathematics	Suraj Singh
Problems and Solutions in Mathematical Statistics	S. C. Gupta, Vikas Gupta & Sanjeev Kumar Gupta
Schaum’s Outline of Statistics	McGraw-Hill (Schaum’s series)

Also Read: IIT JAM 2026 Eligibility Criteria (Subject-Wise)

IIT JAM 2026 Mathematical Statistics Preparation Tips

To prepare for the IIT JAM 2026 Mathematical Statistics paper, candidates must study the topics mentioned in the syllabus of the subject, practise previous years’ question papers, refer to relevant books, and take mock tests. Apart from this general strategy, the following specific preparation tips can help them crack the exam:

1. Prioritise and practise core topics in Mathematics and Statistics. Core topics fir Maths are Calculus, Linear Algebra, Probability, and Differential Equations. For Statistics, give extra time to Estimation, Hypothesis Testing, Regression, and Sampling Distributions.
2. Prepare notes for formulae and theorems for a quick revision. 
3. Take a full-length mock test every weekend to assess the level of their exam preparation. 
4. Revise Mathematics concepts every alternate day. Revise Statistics concepts daily, since they are memory-heavy.

Conclusion

The IIT JAM 2026 Mathematical Statistics syllabus is vast but manageable with the right strategy, books, and consistent practice. Candidates should focus on core concepts, solve previous years’ papers, and take regular mock tests. With smart preparation and revision, they can confidently crack the exam and secure admission.

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