IIT JAM Mathematical Statistics Syllabus 2025, Download Section-Wise Syllabus PDF

IIT JAM Mathematical Statistics Syllabus: Are you looking forward to pursuing MSc in Mathematical Statistics? The IIT JAM exam is a gateway to take admissions in top IITs and study MSc Mathematical Statistics. However, to prepare effectively for the exam, you need to have adequate knowledge regarding IIT JAM Mathematical Statistics Syllabus. This knowledge can help you prioritize topics efficiently. 

IIT JAM Mathematical Statistics Syllabus 2025 

The basic purpose of IIT JAM Mathematical Statistics Syllabus is to assess candidates’ understanding on several IIT JAM Mathematical Statistics topics. The syllabus is designed to evaluate a candidate’s conceptual knowledge. That’s why understanding the syllabus thoroughly is crucial to succeed in the exam. The Mathematical Statistical paper gives 30% weightage to Mathematical concepts and 70% weightage to Statistical concepts. The syllabus covers wide topics including, Statistical Inference, Probability Theory, Calculus, Linear Algebra, Numerical analysis, Real Analysis etc. 

IIT JAM Mathematical Statistics Exam Pattern 

Understanding the IIT JAM Mathematical Statistics exam pattern is important. The three hour exam has 60 questions in total. These 60 questions are divided into three sections; A, B and C. attempting all sections is compulsory for candidates.                              

IIT JAM Mathematical Statistics Exam Pattern
Sections	Type of Questions	No of Questions
A	MCQ	30
B	MSQ	10
C	NAT	20

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Section-wise IIT JAM Mathematical Statistics Syllabus 

Below, is a breakdown of section-wise syllabus for Mathematical Statistics. This knowledge can help you get a good grasp on the topics. 

Section-wise Mathematical Topics 

• Sequence and Series: Cauchy Sequences and Convergences, Real number and sequences, Infinite series and convergences. Comparison test, limit comparison test, Cauchy’s nth root test, Convergence of power series. 
• Differential Calculus of One and Two Variable Numbers: Properties of continuous and differentiable function, Rolle’s theorem and Lagrange’s mean value theorems, Taylor’s theorem with Lagrange’s remainders, global maxima and minima, critical points, local maxima and minima,, Lebnitz’s rule for successive differentiation.
• Integral Calculus: Lebnitz’s rule and its applications,  Fundamental theorems of integral calculus, Beta and Gamma integrals, Transformation of variables, Arc lengths, areas and volumes. 
• Metrics and Determinants: Vector spaces and real fields, Span of a set,  Dimension and basis. Algebra of matrices. Orthogonal and Unitary matrices,  Definition, properties and applications of determinants, Singular and non-singular matrices and their properties. Rank of a matrix, row and column rank. Characteristic roots and Characteristic vectors

Section-wise Statistical Topics 

• Probability: Probability theory, Sample space and algebra of events, Random experiments, Relative frequency, Geometric probability. Conditional probability and Multiplication rule. Pairwise and mutual independence of events.
• Univariate Distribution: Random variables, Cumulative distribution function, Discrete variables, Continuous random variables, Probability mass function, Probability density function, Mathematical expectation and moments,  Jacobian method, Mean, Median, Mode, Standard deviation, Quantiles, Quartiles,  Kurtosis of a probability distribution.
• Standard Univariate Distribution:  Bernoulli, Binomial, Negative binomial, Exponential, Double exponential, beta and gamma. Normal and Cauchy distributions and its properties. 
• Multivariate Distribution: Random vectors definition,  Discrete and continuous type random vectors. Conditional c.d.f. conditional p.d.f. Mathematical expectation of functions of random vectors. Covariance and Correlation.
• Standard Multivariate Distribution: Bivariate normal distribution, marginal and conditional distribution, limit theorems, Weak law of large numbers, Convergence in probability.
• Sampling Distribution: Sampling distribution of a statistic, Random sample, parameter and statistic, Central Student’s t-distribution, Central Chi-square distribution
• Estimation:  Sufficiency of statistics, Complete statistic, Factorization theorem, consistency and relative efficiency of estimators, ao-Blackwell and Lehmann-Scheffe theorems, method of maximum. 
• Testing of Hypothesis: Type-I and Type- II errors, Null and alternative hypotheses,  Level of significance, critical region,  Uniformly most powerful (UMP) tests. 

IIT JAM Mathematical Statistics Syllabus Download PDF 

To get access to the entire IIT JAM Mathematical Statistics Syllabus, you can download the PDF from the official website JAM 2025 IIT Delhi Official Website. Section-wise Syllabus will be mentioned in the PDF. This helps you analyse the topics and align your preparation in a strategic order. 

IIT JAM Mathematical Statistics Best Books

You can get your hands on the best book for Mathematics to cover this section in the IIT JAM Mathematical Statistics syllabus. These books help you grasp all important topics in an easy way.   

Book Name	Author
Mathematical Analysis	Apostol
Mathematical Analysis	SC Malik
Integral Calculus	Dr Gorakh Prasad
Geometry and Vector Calculus	A.R. Vasishtha
Schaum’s Outlines Integral Calculus	Frank Ayres, Elliott Mendelson

IIT JAM Mathematical Statistics Best Books 

To prepare the Statistics section in IIT JAM Mathematical Statistics thoroughly, you need to have the best books for Statistics. These books can help you understand section-wise topics to start your preparation.  

Book Name	Author
Introduction to the Theory of Statistics	Alexander Mood, Franklin Graybill
Fundamentals of Mathematical Statistics	S.C. Gupta and V K Kapoor

 

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