IIT JAM Mathematical Statistics Syllabus 2026
The IIT JAM Mathematical Statistics (MS) syllabus includes topics from both Mathematics and Statistics. The exam syllabus is divided into 12 sections which cover important concepts required for IIT JAM preparation.
Quick Overview
- Mathematics – Sections 1 to 3
- Statistics – Sections 4 to 12
- Important topics include calculus, probability, matrices, distributions and hypothesis testing
Mathematics (Sections 1–3)
1. Sequences and Series
- Sequences of real numbers
- Convergence and limits
- Cauchy sequences
- Monotonic sequences
- Infinite series
- Tests for convergence
- Ratio test
- Root test
- Integral test
- Absolute and conditional convergence
- Power series
2. Differential and Integral Calculus
Differential Calculus- Limits and continuity
- Differentiability
- Rolle’s theorem
- Lagrange mean value theorem
- Taylor and Maclaurin series
- L’Hospital rule
- Maxima and minima
- Fundamental theorem of calculus
- Differentiation under integral sign
- Improper integrals
- Beta and Gamma functions
- Double integrals
- Change of order of integration
- Applications of definite integrals
3. Matrices and Determinants
- Vector spaces
- Linear dependence and independence
- Basis and dimension
- Algebra of matrices
- Symmetric and skew symmetric matrices
- Orthogonal matrices
- Determinants and properties
- Eigenvalues and eigenvectors
- Cayley Hamilton theorem
Statistics (Sections 4–12)
4. Descriptive Statistics and Probability
- Sample and population
- Measures of central tendency
- Mean, median and mode
- Variance and standard deviation
- Moments and skewness
- Correlation
- Random experiments
- Conditional probability
- Bayes theorem
5. Univariate Distributions
- Random variables
- Probability density function
- Probability mass function
- Mathematical expectation
- Moment generating function
- Bernoulli distribution
- Binomial distribution
- Poisson distribution
- Normal distribution
- Gamma distribution
6. Multivariate Distributions
- Random vectors
- Joint distribution
- Marginal distribution
- Conditional distribution
- Covariance and correlation
7. Limit Theorems
- Convergence in probability
- Convergence in distribution
- Law of large numbers
- Central limit theorem
8. Sampling Distributions
- Random samples
- Sampling distribution of statistics
- Order statistics
- Chi square distribution
- t distribution
- F distribution
9. Estimation
- Unbiased estimators
- Sufficiency of statistics
- Method of moments
- Maximum likelihood estimation
- Confidence intervals
10. Testing of Hypothesis
- Null hypothesis
- Alternative hypothesis
- Type I and Type II errors
- Level of significance
- Likelihood ratio tests
11. Non Parametric Methods
- Runs test
- Kolmogorov Smirnov test
- Sign test
- Mann Whitney test
12. Stochastic Processes
- Markov chains
- Transition probability matrix
- Chapman Kolmogorov equation
- Poisson process
Conclusion
The IIT JAM Mathematical Statistics syllabus covers a wide range of topics including calculus, probability, statistical distributions, estimation and hypothesis testing. Understanding each topic thoroughly is essential for cracking the IIT JAM Statistics exam.