IIT JAM 2026 Mathematical Statistics Syllabus: Topic Wise Syllabus, Exam Pattern & Important Books

Result - 20 Mar '26

Updated on Jan 30, 2026 15:30 IST

Are you interested in pursuing MSc in Mathematical Statistics? The IIT JAM 2026 exam is then one of the golden opportunities for the candidates to study MSc Mathematical Statistics from the reputed IIT and NIT institutions. Read this Shiksha article to get the detailed syllabus for the IIT JAM MSc Mathematical Statistics course.

Are you interested in pursuing MSc in Mathematical Statistics? IIT JAM 2026 exam is then one of the golden opportunities for the candidates to study MSc Mathematical Statistics from the reputed IIT and NIT institutions. Read this Shiksha article to get the detailed syllabus for IIT JAM MSc Mathematical Statistics course. Aspirants can also check eligibility criteria & exam pattern for the same here.

IIT Bombay, released the JAM 2026 subject wise syllabus pdf on the official website. Candidates preparing for IIT JAM 2026 Mathematical Statistics course can check out syllabus for the same in this section below. JAM 2026 exam will be successfully concluded on February 15, 2026, at 116 exam centres across nation, for admissions to MSc and Integrated PhD programmes offered at IITs and other participating institutes.

Candidates preparing for the MSc Mathematical Statistics course should advance their studies to get enrol in the prestigious IITs & NIT institutions. Before starting the preparation, the ideal strategy for a candidate should be to analyse the MSc Mathematical Statistics Syllabus and exam pattern for the 2026 session. Candidates can also check IIT JAM eligibility criteria of the MSc Mathematical Statistics course, important topics of Mathematical Statistics, top colleges in IIT JAM exam offering MSc Mathematical Statistics course and other details.

Also Read:

IIT JAM Mathematical Statistics syllabus evaluates the understanding of students in the fundamental and advanced topics. The syllabus is designed to assess that students have the required statistical and mathematical knowledge to complete the MSc in Mathematical Statistics. The syllabus include topics - Probability theory, Statistical inference, Mathematical modeling, Linear algebra, Calculus, Real analysis, Numerical analysis etc.

Table of contents

IIT JAM 2026 Mathematical Statistics Exam Pattern
IIT JAM 2026 Mathematical Statistics Syllabus
Best Books to Study for IIT JAM Mathematical Statistics Preparation 2026
IIT JAM Syllabus 2026 Overview for Mathematical Statistics (MS)
IIT JAM 2026 Mathematical Statistics: Eligibility Criteria
Preparation Tips For IIT JAM 2026 MSc Mathematical Statistics Exam

IIT JAM 2026 Mathematical Statistics Exam Pattern

IIT JAM 2026 Mathematical Statistics exam pattern states that each test paper is of three hours duration. In the exam, candidates need to attempt 60 questions, which were of 100 marks weightage. These 60 questions are divided into three sections – A, B, and C. All these sections are compulsory, and candidates need to attempt questions from all the sections. The medium of instruction for JAM test papers is English.

The detailed IIT JAM exam pattern 2026 is mentioned in the table below:

Section	Type of Questions	No of Question
A	Multiple Choice Questions (MCQs) Each question has four choices with one correct answer.	30
B	Multiple Select Questions (MSQs) Each question has four choices with one or more correct answers.	10
C	Numerical Answer Type (NAT) The answer for each question is a signed real number that needs to be entered using the virtual numeric keypad on the monitor. No choices will be shown for these questions.	20
Total		60

Also Read: IIT JAM Exam Pattern: Exam Paper Pattern, Marking Scheme & Shift Timings

Commonly asked questions

Q: What type of questions does Section B of IIT JAM exam have?

JAM 2026 Examination was conducted for SEVEN subjects, also referred to as Test Papers: Biotechnology (BT), Chemistry (CY), Economics (EN), Geology (GG), Mathematics (MA), Mathematical Statistics (MS), and Physics (PH). The medium for all the Test Papers is English only.

JAM 2026 examination pattern is divided in such a way that the exam was conducted in the form of three sections ie., Section A, B and C.

Section - B contains a total of 10 Multiple Select Questions (MSQs) carrying two marks each. Each MSQ is similar to MCQ but with the difference that MSQ may have one or more than one correct choice (s) out of the four given choices. The candidate is awarded full credit only if all the correct answer (s) and no wrong answers are selected. Candidates can mark the answer (s) by clicking the choice (s). There is no negative marking or partial marking for MSQ.

Q: Will marks be deducted for unanswered questions in IIT JAM 2026?

In IIT JAM 2026 exam pattern, there is no deduction of marks for unanswered questions. Such questions are not taken into consideration while calculating the total marks.

Q: What is the study plan for the preparation of IIT JAM Physics exam?

Physics is one of the most sought course of choice among students who want to take admission in IITs, IISc, etc. It is for this reason alone that IIT JAM Physics paper is extremely competitive. Thus, when preparing for the Physics paper in JAM exam, candidates are suggested to pay less attention to the number of books from which they are studying and more emphasis on finding the topics that will help them score more.

To have an effective prep plan for IIT JAM Physics paper, students should have a timetable in place and make notes of important formulas that will make their last-minute preparation easy.

IIT JAM Physics Study Plan for First Month
Week of Study	Topic to Study	Sub-topic to Study
1	Mechanics and General Properties of Matter-I	Newton’s Laws of Motion and Applications
		Kepler’s Laws
		Polar and Cylindrical Coordinate Systems,
		Conservative and Non-Conservative Forces
		Centrifugal and Coriolis Forces
		Motion Under a Central Force
		Uniformly Rotating Frame
		Gravitational Law and Field
		Velocity and Acceleration in Cartesian
2	Mechanics and General Properties of Matter-II	System of Particles
		Conservation of Linear and Angular Momentum
		Conservation of Energy
		Center of Mass
		Equation of Motion of the Center of Mass
		Elastic and Inelastic Collisions
		Fixed Axis Rotations
		Rigid Body Motion
		Rotation and Translation
		Parallel and Perpendicular Axes Theorem
		Moments of Inertia and Products of Inertia
		Principal Moments and Axes
		Equation of Continuity
		Kinematics of Moving Fluids
		Euler’s Equation
		Bernoulli’s Theorem
3	Mathematical Methods-I	Stokes’ Theorem
		Green’s Theorem
		Divergence Theorem
		Multiple Integrals
		Vector Calculus
		Vector Algebra
		Fourier Series
		Taylor Expansion
		Imperfect and Perfect Differentials
		Jacobian Matrix
		Partial Derivatives
		Calculus of Single and Multiple Variables
4	Mathematical Methods-II	First Order Equations
		Linear Second Order Differential Equations with Constant Coefficients
		Algebra of Complex Numbers
		Matrices and Determinants
IIT JAM Physics Study Plan for Second Month
Week of Study	Topic to Study	Sub-topic to Study
5	Electricity and Magnetism-I	Coulomb’s Law
		Gauss’s Law
		Electric Field and Potential
		Electrostatic Boundary Conditions
		Solution of Laplace’s Equation for Simple Cases
		Capacitors
		Conductors
		Dielectric Polarization
		Electrostatic Energy
		Volume and Surface Charges
6	Oscillations, Waves and Optics-I	Differential Equation for Simple Harmonic Oscillator and Its General Solution
		Superposition of Two or More Simple Harmonic Oscillator
		Damped and Forced Oscillators
		Resonance
7	Oscillations, Waves and Optics-II	Energy Density and Energy Transmission in Waves
		Wave Equation
		Group Velocity and Phase Velocity
		Sound Waves in Media
		Doppler Effect
		Wave Equation
		Fermat’s Principle
8	Oscillations, Waves and Optics-III	General Theory of Image Formation
		Thick Lens, Thin Lens and Lens Combinations
		Fraunhofer Diffraction
		Rayleigh Criterion and Resolving Power
		Diffraction Gratings
		Polarization
		Double Refraction and Optical Rotation

IIT JAM 2026 Mathematical Statistics Syllabus

These topics are essential for students who plan to pursue a career in mathematical statistics, which is a rapidly growing field with applications in a wide range of industries, including finance, insurance, healthcare, and government. Specifically, IIT JAM Mathematical Statistics syllabus 2026 is designed to prepare students for conducting original research in mathematical statistics, applying statistical methods to real-world problems, teaching mathematical statistics at the college or university level, and working as a statistician in industry or government.

Aspirants preparing for IIT JAM MSc Mathematical Statistics degree programme should start their preparation according to the Mathematical Statistics syllabus mentioned below:

The Mathematical Statistics (MS) Test Paper comprises following topics of Mathematics (about 30% weight) and Statistics (about 70% weight).

Mathematics

Sequences and Series of real numbers: Sequences of real numbers, their convergence, and limits. Cauchy sequences and their convergence. Monotonic sequences and their limits. Limits of standard sequences. Infinite series and its convergence, and divergence. Convergence of series with non- negative terms. Tests for convergence and divergence of a series. Comparison test, limit comparison test, D’Alembert’s ratio test, Cauchy’s n th root test, Cauchy’s condensation test and integral test. Absolute convergence of series. Leibnitz’s test for the convergence of alternating series. Conditional convergence. Convergence of power series and radius of convergence.

Differential Calculus of one and two real variables: Limits of functions of one real variable. Continuity and differentiability of functions of one real variable. Properties of continuous and

differentiable functions of one real variable. Rolle's theorem and Lagrange's mean value theorems. Higher order derivatives, Lebnitz's rule and its applications. Taylor's theorem with Lagrange's and Cauchy's form of remainders. Taylor's and Maclaurin's series of standard functions. Indeterminate forms and L' Hospital's rule. Maxima and minima of functions of one real variable, critical points, local maxima and minima, global maxima and minima, and point of inflection. Limits of functions of two real variables. Continuity and differentiability of functions of two real variables. Properties of continuous and differentiable functions of two real variables. Partial differentiation and total differentiation. Lebnitz's rule for successive differentiation. Maxima and minima of functions of two real variables. Critical points, Hessian matrix, and saddle points. Constrained optimization techniques (with Lagrange multiplier).

Integral Calculus: Fundamental theorems of integral calculus (single integral). Lebnitz's rule and its applications. Differentiation under integral sign. Improper integrals. Beta and Gamma integrals:
properties and relationship between them. Double integrals. Change of order of integration. Transformation of variables. Applications of definite integrals. Arc lengths, areas and volumes.
Matrices and Determinants: Vector spaces with real field. Subspaces and sum of subspaces. Span of a set. Linear dependence and independence. Dimension and basis. Algebra of matrices. Standard matrices (Symmetric and Skew Symmetric matrices, Hermitian and Skew Hermitian matrices, Orthogonal and Unitary matrices, Idempotent and Nilpotent matrices). Definition, properties and applications of determinants. Evaluation of determinants using transformations. Determinant of product of matrices. Singular and non-singular matrices and their properties. Trace of a matrix.
Adjoint and inverse of a matrix and related properties. Rank of a matrix, row-rank, column-rank, standard theorems on ranks, rank of the sum and the product of two matrices. Row reduction and
echelon forms. Partitioning of matrices and simple properties. Consistent and inconsistent system of linear equations. Properties of solutions of system of linear equations. Use of determinants in
solution to the system of linear equations. Cramer’s rule. Characteristic roots and Characteristic vectors. Properties of characteristic roots and vectors. Cayley Hamilton theorem.

Statistics
Probability: Random Experiments. Sample Space and Algebra of Events (Event space). Relative frequency and Axiomatic definitions of probability. Properties of probability function. Addition
theorem of probability function (inclusion exclusion principle). Geometric probability. Boole's and Bonferroni's inequalities. Conditional probability and Multiplication rule. Theorem of total
probability and Bayes’ theorem. Pairwise and mutual independence of events.
Univariate Distributions: Definition of random variables. Cumulative distribution function (c.d.f.) of a random variable. Discrete and Continuous random variables. Probability mass function (p.m.f.)
and Probability density function (p.d.f.) of a random variable. Distribution (c.d.f., p.m.f., p.d.f.) of a function of a random variable using transformation of variable and Jacobian method. Mathematical expectation and moments. Mean, Median, Mode, Variance, Standard deviation, Coefficient of variation, Quantiles, Quartiles, Coefficient of Variation, and measures of Skewness and Kurtosis of a probability distribution. Moment generating function (m.g.f.), its properties and uniqueness. Markov and Chebyshev inequalities and their applications.

Standard Univariate Distributions: Degenerate, Bernoulli, Binomial, Negative binomial, Geometric, Poisson, Hypergeometric, Uniform, Exponential, Double exponential, Gamma, Beta (of first and

second type), Normal and Cauchy distributions, their properties, interrelations, and limiting (approximation) cases.

Multivariate Distributions: Definition of random vectors. Joint and marginal c.d.f.s of a random vector. Discrete and continuous type random vectors. Joint and marginal p.m.f., joint and marginal

p.d.f.. Conditional c.d.f., conditional p.m.f. and conditional p.d.f.. Independence of random variables. Distribution of functions of random vectors using transformation of variables and Jacobian method. Mathematical expectation of functions of random vectors. Joint moments, Covariance and Correlation. Joint moment generating function and its properties. Uniqueness of joint m.g.f. and its applications. Conditional moments, conditional expectations and conditional variance. Additive properties of Binomial, Poisson, Negative Binomial, Gamma and Normal Distributions using their m.g.f..

Standard Multivariate Distributions: Multinomial distribution as a generalization of binomial distribution and its properties (moments, correlation, marginal distributions, additive property). Bivariate normal distribution, its marginal and conditional distributions and related properties. Limit Theorems: Convergence in probability, convergence in distribution and their inter relations. Weak law of large numbers and Central Limit Theorem (i.i.d. case) and their applications.

Sampling Distributions: Definitions of random sample, parameter and statistic. Sampling distribution of a statistic. Order Statistics: Definition and distribution of the rth order statistic (d.f.

and p.d.f. for i.i.d. case for continuous distributions). Distribution (c.d.f., p.m.f., p.d.f.) of smallest and largest order statistics (i.i.d. case for discrete as well as continuous distributions). Central Chi-

square distribution: Definition and derivation of p.d.f. of central χ2 distribution with n degrees of freedom (d.f.) using m.g.f.. Properties of central χ2 distribution, additive property and limiting form

of central χ2 distribution. Central Student's t-distribution: Definition and derivation of p.d.f. of Central Student's t-distribution with n d.f., Properties and limiting form of central t-distribution.

Snedecor's Central F-distribution: Definition and derivation of p.d.f. of Snedecor's Central F- distribution with (m, n) d.f.. Properties of Central F-distribution, distribution of the reciprocal of F-

distribution. Relationship between t, F and χ2 distributions.

Estimation: Unbiasedness. Sufficiency of a statistic. Factorization theorem. Complete statistic. Consistency and relative efficiency of estimators. Uniformly Minimum variance unbiased estimator (UMVUE). Rao-Blackwell and Lehmann-Scheffe theorems and their applications. Cramer-Rao inequality and UMVUEs. Methods of Estimation: Method of moments, method of maximum

likelihood, invariance of maximum likelihood estimators. Least squares estimation and its applications in simple linear regression models. Confidence intervals and confidence coefficient. Confidence intervals for the parameters of univariate normal, two independent normal, and exponential distributions.

Testing of Hypotheses: Null and alternative hypotheses (simple and composite), Type-I and Type- II errors. Critical region. Level of significance, size and power of a test, p-value. Most powerful

critical regions and most powerful (MP) tests. Uniformly most powerful (UMP) tests. Neyman Pearson Lemma (without proof) and its applications to construction of MP and UMP tests for parameter of single parameter parametric families. Likelihood ratio tests for parameters of univariate normal distribution.

Candidates can check out the JAM 2026 syllabus fo other subjects from here:

JAM Biotechnology Syllabus	IIT JAM Economics Syllabus	JAM Mathematics Syllabus
JAM Physics Syllabus	IIT JAM Chemistry Syllabus	IIT JAM Geology Syllabus

Also Read: IIT JAM Chapter Wise Weightage; Know Important Topics

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Best Books to Study for IIT JAM Mathematical Statistics Preparation 2026

Aspirants can go through topic-wise books that they can refer to when they are preparing for IIT JAM Mathematical Statistics paper below.

IIT JAM Mathematical Statistics Books to Read for Mathematics

Books that aspirants should consider reading for topics in the Mathematics section of the exam are mentioned below:

Name of the Book	Author
Mathematical Analysis	S.C. Malik
Mathematical Analysis	Apostol
Principle of Mathematical Analysis	Rudi
Schaum’s Outlines Integral Calculus	Frank Ayres, Elliott Mendelson
Integral Calculus	Dr Gorakh Prasad
Vector Analysis: Schaum’s Outlines Series	Murray Spiegel, Seymour Lipschutz, Dennis Spellman
Geometry and Vector Calculus	A.R. Vasishtha
Ordinary Differential Equation	Peter J. Collins, G.F. Simmons, M.D. Raisinghania

IIT JAM Syllabus 2026 Overview for Mathematical Statistics (MS)

The JAM test paper for Mathematical Statistics consists of two subjects which are Mathematics and Statistics. The weightage given to Mathematics is 40 per cent and Statistics is 60 per cent. Aspirants can go through the detailed IIT JAM Mathematical Statistics syllabus here. Find out the important topics for the Mathematical Statistics course below:

IIT JAM 2026 Mathematics Syllabus

Sequences and Series: Convergence of sequences of real numbers, Comparison, root and ratio tests for convergence of series of real numbers.
Differential Calculus: Limits, continuity, and differentiability of functions of one and two variables. Rolle's theorem, mean value theorems, Taylor's theorem, indeterminate forms, maxima and minima of functions of one and two variables.
Integral Calculus: Fundamental theorems of integral calculus. Double and triple integrals, applications of definite integrals, arc lengths, areas, and volumes.
Matrices: Rank, inverse of a matrix, Systems of linear equations, Linear transformations, eigenvalues, and eigenvectors. Cayley-Hamilton theorem, symmetric, skew-symmetric, and orthogonal matrices.

IIT JAM 2026 Statistics Syllabus

Probability: Axiomatic definition of probability and properties, conditional probability, multiplication rule. The theorem of total probability. Bayes’ theorem and independence of events.
Random Variables: Probability mass function, probability density function, and cumulative distribution functions, distribution of a function of a random variable. Mathematical expectation, moments, and moment generating function. Chebyshev's inequality.
Standard Distributions: Binomial, negative binomial, geometric, Poisson, hypergeometric, uniform, exponential, gamma, beta, and normal distributions. Poisson and normal approximations of a binomial distribution.
Joint Distributions: Joint, marginal, and conditional distributions. Distribution of functions of random variables. Joint moment generating function. Product moments, correlation, simple linear regression. Independence of random variables.
Sampling Distributions: Chi-square, t and F distributions, and their properties.
Limit Theorems: Weak law of large numbers. Central limit theorem (i.i.d.with finite variance case only).
Estimation: Unbiasedness, consistency, and efficiency of estimators, method of moments, and method of maximum likelihood. Sufficiency, factorization theorem. Completeness, Rao-Blackwell, and Lehmann-Scheffe theorems, uniformly minimum variance unbiased estimators. Rao-Cramer inequality. Confidence intervals for the parameters of univariate normal, two independent normal, and one parameter exponential distributions.
Testing of Hypotheses: Basic concepts, applications of Neyman-Pearson Lemma for testing simple and composite hypotheses. Likelihood ratio tests for parameters of univariate normal distribution.

Click Here: IIT JAM 2026 Mathematics Statistics Syllabus PDF

IIT JAM Mathematical Statistics Books to Read for Statistics

Books that aspirants should consider reading for topics in the Statistics section of the exam are mentioned below:

Name of the Book	Author
Introduction to the Theory of Statistics	Alexander Mood, Franklin Graybill, Duane Boes
An Introduction to Probability and Statistics	V.K. Rohatgi

Apart from the above-mentioned books, aspirants should also go through the books mentioned below to prepare for IIT JAM exam for Mathematical Statistics.

Name of the Book	Author
IIT JAM: MSc Mathematical Statistics	Anand Kumar
Complete Resource Manual MSc Mathematics	Suraj Singh
Fundamental of Mathematical Statistics	S.C. Gupta & V.K. Kapoor
Introduction to Mathematical Statistics	Robert V. Hogg and Craig Mckean Hogg

Commonly asked questions

Q: Which books are best for IIT JAM maths?

The key texts for the IIT JAM Mathematics exam are: Principles of Real Analysis by S. C. Malik for Real Analysis; Linear Algebra by H. Anton or by Seymour Lipschitz from the Schaum's outline series for Linear Algebra; Integral Calculus - F. Ayres, or GorakhPrasad's Textbooks for Integral Calculus; For Differential Equations, either M.D. Raisinghania will work, or for excellent, Modern Algebra by A. R. Vasishtha or by Joseph A. Gallian will work fine.

Q: What are the best books for IIT JAM 2026 exam preparation specifically for Mathematics Statistics subject?

These are some of the best books for IIT JAM 2026 exam preparation specifically for Mathematics Statistics subject:

Name of the Book	Author
IIT JAM: MSc Mathematical Statistics	Anand Kumar
Complete Resource Manual MSc Mathematics	Suraj Singh
Fundamental of Mathematical Statistics	S.C. Gupta & V.K. Kapoor
Introduction to Mathematical Statistics	Robert V. Hogg and Craig Mckean Hogg
Problems and Solutions in Mathematical Statistics	S.C Gupta, Vikas Gupta and Sanjeev Kumar Gupta

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IIT JAM 2026 Mathematical Statistics: Eligibility Criteria

Candidates can check the minimal eligibility criteria for enrolling in the MSc Mathematical Statistics course from below:

Test Paper Code	Academic Programmes	Institutes	Minimal Educational Qulaifucation for Admissions
Mathematical Statistics (MS)	MSc Mathematical Statistics, Operation & Research	IIT Bombay,	No Restrictions
	MSc Mathematical Statistics	IIT Palakkad	At least four Mathematics courses in Bachelor’s degree.
	MSc Mathematical Statistics	IIT Tirupati	No Restrictions.

IIT JAM 2026 Student Reactions

The JAM 2026 exam will be held on February 15, 2026, at various exam centres across the country. For better preparation and knowledge of the JAM exam difficulty level, candidates appearing for IIT JAM 2026 exam can check out the previous year's student reaction video from here:

Also Read: Check Year Wise IIT JAM Student Reaction and Difficulty Level from Here

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Preparation Tips For IIT JAM 2026 MSc Mathematical Statistics Exam

These are the tips students should follow:

Before preparing for the MSc Mathematical Statistics exam, students should know exam pattern & syllabus.
After knowing these details, create study plan & try to follow it.
There are many books and online resources available to help you prepare for the MSc Mathematical Statistics exam.
Take notes on the important concepts and ideas. This will help you to remember the information more easily.

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