# IIT JAM Mathematical Statistics Syllabus 2023

IIT JAM mathematical statistics syllabus for 2023 is divided into two parts namely i.e. statistics and mathematics. The weightage for statistics is 60% and for mathematics is 40%.  Listed below are some of the topics of IIT JAM mathematical statistics syllabus:

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, inverse of a matrix. systems of linear equations. Linear transformations, eigenvalues and eigenvectors. Cayley-Hamilton theorem, symmetric, skewsymmetric and orthogonal matrices.

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.

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 normal, and one parameter exponential distributions.

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.

Differential Equations: Ordinary differential equations of the first order of the form y’ = f(x,y). Linear differential equations of the second order with constant coefficients.

Statistics Probability: Axiomatic definition of probability and properties, conditional probability, multiplication rule. Theorem of total probability. Bayes’ theorem and independence of events.

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. 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).

## IIT JAM Mathematical Statistics 2023 Exam Pattern

 Events Details Total Duration of the Test 3 hours Total number of questions 60 Number of Section 3 (Sec A, B and C) Question Type for the Test MCQ, MSQ and NAT Marks in Total 100

## IIT JAM Mathematical Statistics Books for Preparation

 Section Book Name Author Mathematical Statistics IIT-JAM: M.Sc. Mathematical Statistics Joint Admission Test Anand Kumar Mathematics A Complete Resource Manual M.Sc Mathematics Entrance examination Suraj Singh and Reshmi Gupta Mathematical Statistics Fundamentals of Mathematical Statistics S.C. Gupta and V K Kapoor Mathematical Statistics Introduction to Mathematical Statistics Hogg Statistics An Introduction to Probability and Statistics Vijay K. Rohatgi and A.K. Md. Ehsanes Saleh