From the Academic Session 2004-05, IITs started conducting a Joint Admission Test for M.Sc. (JAM). 

There are many MSc entrance exams held across India and IIT JAM is the most popular among them.

The objective of JAM is to provide admissions to M.Sc. (Two Years), Joint M.Sc.-Ph.D., M.Sc.-Ph.D. Dual Degree, and other Post-Bachelor Degree Programmes at the IITs and Integrated Ph.D. Degree Programmes at the IISc and to consolidate Science as a career option for bright students across the country. 

IIT JAM Examination is conducted in six subjects, also referred to as Test Papers; Biotechnology (BT), Chemistry (CY), Geology (GG), Mathematics (MA), Mathematical Statistics (MS) and Physics (PH).

IIT JAM Mathematical statistics come with a bright future scope. Data scientist, data analyst, Quality analyst, Data Engineer, etc are some of the jobs offered to students from the statistical backgrounds.

In this post, we will briefly give the syllabus of IIT JAM mathematical statistics.


1. IIT JAM Syllabus for Statistics

2. The pattern of IIT JAM Statistics Test Papers

3. IIT JAM Mathematical Statistics previous year papers

4. Opening and Closing Ranks for IIT JAM 2020

5. IIT JAM Mathematical Statistics Seats from IITs

6. Useful Tips for preparation of IIT JAM exam Mathematical Statistics

IIT JAM Syllabus for Statistics:

The Mathematical Statistics (MS) test paper comprises of Mathematics (40% weightage) and Statistics (60% weightage). 

Mathematics 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, the inverse of a matrix. Systems of linear equations. Linear transformations, eigenvalues, and eigenvectors. Cayley-Hamilton theorem, symmetric, skew-symmetric, and orthogonal matrices. 

Statistics 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 normals, 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.

Topic-wise Marks Distribution of IIT JAM Mathematics Statistics

The pattern of IIT JAM Statistics Test Papers:

The JAM 2020 Examination for all the six test papers will be carried out as ONLINE Computer Based Test (CBT) where the candidates will be shown the questions in a random sequence on a computer screen. 

For all the six test papers, the duration of the examination will be 3 hours. The medium for all the test papers will be English only.

There will be a total of 60 questions carrying 100 marks. The entire paper will be divided into three sections, A, B, and C. All sections are compulsory. Questions in each section will be of different types as given below:

Section–A contains a total of 30 Multiple Choice Questions (MCQs) involving 10 questions of one mark each and 20 questions of two marks each.

Each MCQ has four choices out of which only one choice is the correct answer. Candidates can mark the answer by clicking the choice.

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 gets full credit only if he/she selects all the correct answer(s) only and no wrong answers. Candidates can mark the answer(s) by clicking the choice(s).

Section–C contains a total of 20 Numerical Answer Type (NAT) questions involving 10 questions of one mark each and 10 questions of two marks each. 

For these NAT type questions, the answer is a signed real number, which needs to be entered using the virtual numeric keypad on the monitor. No choices will be shown for NAT questions.

In all sections, questions not attempted will result in zero marks. 

In Section-A (MCQ), the wrong answer will result in negative marks. For each wrong answer to 1 mark questions, 1/3 mark will be deducted and similarly, for each wrong answer to 2 marks questions, 2/3 mark will be deducted.

In Section-B (MSQ), there are no negative and no partial marking provisions. There is no negative marking in Section-C (NAT) as well.

There is a provision of using the online virtual calculator. The candidates, therefore, should not bring any calculator with them.

Mobile phones or any other electronic devices are strictly prohibited inside the examination hall. Charts, graph sheets, and tables are also NOT allowed inside the examination hall.

A scribble pad will be provided for rough work and this has to be returned back at the end of the examination.

The candidates are required to select the answer for MCQ and MSQ type questions using the mouse. The answer for NAT questions can be entered using a virtual numeric keypad (the keyboard of the computer will be disabled).

At the end of the 3 hours, the computer will automatically end the examination.

IIT JAM Mathematical Statistics previous year papers:

1. IIT JAM Statistics Question Paper year 2017

2. IIT JAM Statistics Question Paper year 2018

3. IIT JAM Statistics Question Paper year 2019

4. IIT JAM Statistics Question Paper year 2020 (answer key)

IIT JAM Mathematical Statistics Seats from IITs

The competition is very high for IIT JAM Mathematical Statistics because there are limited seats in two IITs for statistics and there are 3500+ candidates who apply for the IIT JAM Mathematical statistic every year.


Total Seats

IIT Bombay


IIT Kanpur




Opening and Closing Ranks for IIT JAM 2020:

1. JAM 2019 Round 1 (First) Opening and Closing Ranks

2. JAM 2019 Round 2 (Second) Opening and Closing Ranks

3. JAM 2019 Round 3 (Final) Opening and Closing Ranks

Useful Posts for preparation of IIT JAM exam:

10 Tips and tricks to prepare for entrance exams

Pomodoro Technique: How to study more in less time?

6 ways to boost your performance in the exam

Some Useful Books for IIT JAM Mathematical Statistics papers:

Some topic wise IIT JAM Mathematical Statistics Books that will help you to prepare better.


IIT JAM Mathematical Statistics Books Name

Author Name


Fundamentals of Mathematical statistics

S.C. Gupta & V.K. Kapoor

An introduction to probability and statistics

V.K. Rohatgi

Introduction to Mathematical statistics

Robert V. Hogg and Craig Mckean Hogg

Introduction to the theory of statistics

Mood and Graybill

Previous Year Papers

M.Sc. Mathematical Statistics

Anand Kumar


The elements of Real Analysis

Dr. Shanti Narayan

More about IIT JAM 2021: IIT JAM 2021 Exam Dates, Syllabus, Application Form, Result

All the best for your IIT JAM Exam 2021.

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