IIT JAM 2025 Mathematical Statistics Syllabus: Topic Wise Syllabus, Exam Pattern & Important Books

11 mins read2.4K Views

Exam On: 2 Feb '25

Associate Senior Executive

Updated on Jul 26, 2024 10:34 IST

Are you interested in pursuing MSc in Mathematical Statistics? The IIT JAM 2025 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. Aspirants can also check the eligibility criteria and exam pattern for the same here.

IIT Delhi, released the JAM 2025 subject wise syallbus pdf on the official website. Candidates preparing for IIT JAM 2025 Mathematical Statistics course can check out the syllabus for the same in this section below. JAM 2025 exam will be held on February 2, 2025 at 115 exam centres across the nation.

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 analyze the MSc Mathematical Statistics Syllabus and exam pattern for the 2025 session. Candidates can also check the IIT JAM eligibility criteria of the MSc Mathematical Statistics course, important topics of Mathematical Statistics, top colleges in the IIT JAM exam offering MSc Mathematical Statistics course and other details.

Also Read:

The purpose of the IIT JAM Mathematical Statistics syllabus is to assess a candidate's understanding of fundamental concepts and advanced topics in the field of mathematical statistics. The JAM 2025 Mathematical Statistics syllabus is designed to ensure that students admitted to the MSc in Mathematical Statistics program at JAM 2025 result sharing institutes have the necessary mathematical and statistical knowledge to succeed in their studies and research. The syllabus covers a wide range of topics, including Probability theory, Statistical inference, Mathematical modeling, Linear algebra, Calculus, Real analysis, Numerical analysis etc.

IIT JAM 2025 Mathematical Statistics Exam Pattern

IIT JAM 2025 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.

Explore colleges based on IIT JAM

Indian Institute of Science institute image

Bangalore

Courses Offered6 courses4.2

Total Fees Range₹32 K - 48 K

In Top 10 %ile by Average Salary of M.Sc. Colleges

Birla Institute of Technology, Mesra institute image

Ranchi

Courses Offered4 courses4.0

Total Fees Range₹2.58 L - 3.49 L

In Top 10 %ile by Average Salary of M.Sc. Colleges

Sant Longowal Institute of Engineering and Technology institute image

Sangrur

Courses Offered3 courses

Total Fees Range₹46 K

In Top 10 %ile by Average Salary of M.Sc. Colleges

Parul University institute image

Vadodara

Courses Offered2 courses

Total Fees Range₹2.1 L

In Top 10 %ile by Average Salary of M.Sc. Colleges

Want better recommendations?

There is a 90% more chance of getting best college recommendations by sharing preferences.

+ Add preferences

IIT Madras - Indian Institute of Technology institute image

Chennai

Courses Offered3 courses4.3

Total Fees Range₹20 K

In Top 10 %ile by Average Salary of M.Sc. Colleges

IIT Bombay - Indian Institute of Technology institute image

Mumbai

Courses Offered7 courses4.5

Total Fees Range₹2.69 L

In Top 10 %ile by Average Salary of M.Sc. Colleges

IIT Patna - Indian Institute of Technology institute image

Patna

Courses Offered3 courses4.0

Total Fees Range₹60 K

In Top 10 %ile by Average Salary of M.Sc. Colleges

IIT Kharagpur - Indian Institute of Technology institute image

Kharagpur

Courses Offered18 courses4.5

Total Fees Range₹42.66 K

In Top 10 %ile by Average Salary of M.Sc. Colleges

IIT Kanpur - Indian Institute of Technology institute image

Kanpur

Courses Offered5 courses4.5

Total Fees Range₹12 K

In Top 10 %ile by Average Salary of M.Sc. Colleges

IISER Bhopal - Indian Institute of Science Education & Research institute image

Bhopal

Courses Offered3 courses5.0

Total Fees RangeNA

In Top 10 %ile by Average Salary of M.Sc. Colleges

View allCollections

The detailed IIT JAM exam pattern 2025 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 2025 Exam Pattern: Exam Paper Pattern, Marking Scheme & Shift Timings

IIT JAM 2025 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, the IIT JAM Mathematical Statistics syllabus 2025 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.

Q: Which are the best books for IIT JAM Biotechnology preparation 2025?

Aspirants can go through important books that they should consider studying from when they are preparing for the IIT JAM Biotechnology exam.

Books for IIT JAM Biotechnology
Biochemistry	Donald Voet & Judith G Voet
Biochemistry	AL Lehninger
Analytical Biochemistry	Holme
Biochemistry	Zubay
Principles of Biochemistry	Lehninger
Cell and Molecular Biology -Concepts and Experiments	John Wiley & Sons, Inc., USA

Note: The information is sourced from the official body and may vary.

Aspirants preparing for the 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 2025 syllabus fo other subjects from here:

JAM 2025 Biotechnology Syllabus	IIT JAM 2025 Economics Syllabus	JAM 2025 Mathematics Syllabus
JAM 2025 Physics Syllabus	IIT JAM 2025 Chemistry Syllabus	IIT JAM 2025 Geology Syllabus

Also Read: IIT JAM 2025 Chapter Wise Weightage; Know Important Topics

Best Books to Study for IIT JAM Mathematical Statistics Preparation 2025

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

Explore more Science exams with upcoming dates

TIFR GS

TIFR GS 2025 Exam

8 Dec '24

ICAR AIEEA

ICAR AIEEA PG 2024 Counselling...

6 Jan '25 - 10 Jan '25

CCMN

IIT JAM 2025 Exam Date

2 Feb '25

CUET-PG

CUET PG 2025 Application Proce...

26 Dec '24 - 5 Feb '25

FRI Entrance Exam

FRI Entrance Exam 2025 Applict...

4 Feb '25 - 8 Apr '25

NSI Admission Test

NSI Admission Test 2025 Appli...

20 Apr '25 - 20 May '25

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 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 2022.

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

CUET PG 2025 Mathematical Statistics: Eligibility Criteria

Candidates can check the minimal eligibility criteria for enrolling in MSc Mathemtical 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 2025 Student Reactions

The JAM 2025 exam will be held on February 2, 2025, at various exam centres across the country. For better preparation and knowledge of the JAM exam difficulty level candidates appearing for the IIT JAM 2025 exam can check out the previous year's (2024) student reaction video from here:

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

Preparation Tips For IIT JAM 2025 MSc Mathematical Statistics Exam

Here are some tips that aspirants can refer to while preparing for MSc Mathematical Statistics exam:

Understand the syllabus and exam pattern: The first step is to thoroughly understand the syllabus and exam pattern for the MSc Mathematical Statistics exam. This will help you to focus your studies and identify the topics that you need to cover in more detail.
Make a study plan: Once you understand the syllabus and exam pattern, you can create a study plan. This plan should be realistic and achievable, and it should break down the syllabus into manageable chunks.
Use good study materials: There are many books and online resources available to help you prepare for the MSc Mathematical Statistics exam. Choose study materials that are comprehensive and up-to-date.
Take notes: As you study, take notes on the important concepts and ideas. This will help you to remember the information more easily.

Read More:

About the Author

Manisha Kumari

Associate Senior Executive

Being a post-graduate and BEd degree holder, I'm an innovative, task-driven and immensely motivated science enthusiast, making me a passionate content writer. I love providing meaningful and constructive articles in... Read Full Bio

Download Important Dates for Science Exams