IIT JAM Mathematical Statistics (MS) 2024: Exam Date, Syllabus, Question Papers, Important Topics
IIT JAM Mathematical Statistics (MS) 2025 will be held on 2nd February 2025 (Afternoon Session). Candidates can check out all details about the exam, like important dates, syllabus, previous year cutoffs, previous year papers, FAQs, etc., here.
IIT JAM 2025 Mathematical Statistics exam will be conducted on February 2nd, 2025 (Afternoon Session). The IIT JAM admit card 2025 will be published in early January 2025 (tentative). IIT JAM Mock Test 2025 link has been activated and candidates can use it for their preparation. IIT Madras has released mock tests for Biotechnology, Geology, Chemistry, Economics, IIT JAM 2025 Mathematical Statistics, Mathematics, and Physics. Practising mock tests will be a great help for the candidates who are going to appear for the IIT JAM Mathematical Statistics. Students will be able to understand, the exam pattern, marking scheme, and difficulty level of the exam when a candidate practices mock tests.
Download: IIT JAM Admit Card 2025
IIT JAM 2025 admit card has been issued today, January 8, 2025. Candidates who have successfully completed and submitted the IIT JAM 2025 application form have been issued the admit cards. Candidates must login in the JOAPS portal with their enrolment ID and password to download the IIT JAM admit card. The IIT JAM 2025 admit card is a required document that must be carried on the IIT JAM 2025 exam day. Candidates can download their IIT JAM admit card from the direct link provided above.
The Indian Institute of Technology (IIT) Madras has released IIT JAM previous year question papers with solutions.. Students who have submitted the JAM application form and are preparing for the examination can practise the JAM previous year question papers for JAM Mathematical Statistics with only two months until the exam. As a result, candidates must complete the prescribed JAM 2025 syllabus and prepare for the exam. The previous year's IIT JAM Mathematical Statistics question papers are available on the official website jam.iitm.ac.in.Solving previous year question papers can help candidates assess their preparation and identify areas for improvement.
IIT JAM 2025 is used to get admission to M.Sc. and PhD programmes at various technical institutes. IIT JAM Mathematical Statistics ranks as one of the prominent subjects in which you can pursue a career. The competition for IIT JAM 2023 Mathematical Statistics is high because statistics seats are limited in two IITs and over 2000 candidates apply each year and there are 110 seats available (IIT Kanpur: 62 and IIT Bombay: 48).
The application of mathematics to statistics is referred to as mathematical statistics. Statistics is a method for analysing and collecting large amounts of numerical data. Candidates must carefully go over the section-by-section syllabus of IIT JAM Mathematical Statistics 2025 to get a complete overview. Candidates should also be aware that the IIT JAM Exam question paper will be divided into three sections and will include three types of questions: MCQ, MSQ, and NAT. Read on to learn more about IIT JAM 2025 Mathematical Statistics syllabus, previous year question papers, and cutoff.
IIT JAM 2025 Mathematical Statistics Dates
Candidates can check out all the IIT JAM Mathematical Statistics 2025 important dates in the table provided below:
Events | Dates (Tentative) |
IIT JAM 2025 Online Application Processing System (JOAPS) Website Opens | 3rd September, 2024 |
IIT JAM 2025 Last Date for Closing Registration | 11th October, 2024 |
To Upload a Valid OBC-NCL/EWS Certificate | 20th November, 2024 |
Last Date to Change the Examination Cities/Test Papers/ Category/ Gender | 30th November, 2024 |
IIT JAM 2025 Application Form Correction Window | To be Notified |
Confirmation of Compensatory Time/Scribe Assistants | 30th December, 2024 |
IT JAM 2025 Admit Card Availability on the Online Application Portal | Early January, 2025 |
IIT JAM 2025 Exam Date | 2nd February, 2025 |
IIT JAM 2025 Provisional Answer Key | To be Notified |
IIT JAM 2025 Response Sheet | To be Notified |
IIT JAM Provisional Answer Key Challenge Window | To be Notified |
Announcement of IIT JAM 2025 Result | 16th March, 2025 |
IIT JAM 2025 Final Answer Key | To be Notified |
IIT JAM 2025 Counseling Registration | To be Notified |
IIT JAM 2025 Scorecard Availability | 25th March, 2025 |
IIT JAM 2025 Portal for Admission Opens | 2nd April,2025 |
IIT JAM 2025 Admission Form Correction (Last Date) | To be Notified |
IIT JAM Mathematical Statistics 2025 Syllabus
Candidates can check out the list of total topics and sub-topics in the IIT JAM Mathematical Statistics 2025 Syllabus which is divided into 2 parts Mathematics and Statistics:
Mathematics (about 30% weightage)
Statistics (about 70% weightage)
IIT JAM Mathematical Statistics 2025 Syllabus: Mathematics
IIT JAM Mathematics Statistics syllabus 2025 is provided below:
Topics | Sub-topics |
|---|---|
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 nth 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. |
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. |
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). |
Matrices and Determinants: | Vector spaces with real fields. 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 systems 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. |
IIT JAM Mathematical Statistics 2025 Syllabus: Statistics
IIT JAM Mathematics Statistics syllabus has been given below:
Topics | Sub-topics |
|---|---|
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. |
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. |
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. |
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.. |
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. |
Standard Multivariate Distributions | Multinomial distribution as a generalisation of binomial distribution and its properties (moments, correlation, marginal distributions, additive property). Bivariate normal distribution, its marginal and conditional distributions and related properties. |
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- F-distribution. Relationship between t, F and χ2 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 parameters of single parameter parametric families. Likelihood ratio tests for parameters of univariate normal distribution. |
Estimation | Unbiasedness. Sufficiency of a statistic. Factorization theorem. Complete statistics. 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. |
Students can also check: IIT JAM Mathematical Statistics 2024 Syllabus PDF
IIT JAM Mathematical Statistics Previous Question Papers
Students can check out the IIT JAM Mathematical Statistics previous year question papers from 2015-2023 in the table provided below:
Previous Year Question Papers | Answer Key |
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Also Read: IIT JAM 2025 Exam Pattern
IIT JAM Mathematical Statistics Cutoff
IIT JAM cutoff varies each year based on the level of the questions, the total number of applicants, and the total number of seats. Knowing the cutoff marks is important because it will help you set your goals and plan your studies. IIT JAM Mathematical Statistics 2025 cutoff will be updated here as soon as it is released by IIT Madras. Students can get an idea of the minimum marks by looking at the table below, which shows the IIT JAM 2024 Mathematical Statistics cutoff.
Category | IIT JAM 2024 Physics Cutoff |
General | 23.03 |
EWS/OBC | 20.72 |
SC/ST/PWD | 11.51 |
Also Check: IIT JAM 2025 Preparation Strategy, Tips, Study Plan, Timetable
It is not difficult to qualify for any entrance exam, such as the IIT JAM Exam. You can easily pass the exam with proper planning and strategy. Your chances of success will improve if you achieve a master's degree from IITs or IISC.
For more information and the latest updates on IIT JAM 2025 stay tuned with CollegeDekho.