IIT JAM 2019 Syllabus for Mathematical Statistics (MS)

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Syllabus of Mathematical Statistics – IIT JAM 2019


Sequences and Series

Comparison, the convergence of sequences of real numbers, root and ratio tests for convergence of series of real numbers;

Differential Calculus

Rolle’s theorem, mean value theorems, Taylor’s theorem; Limits, continuity and differentiability of functions of one and two variables; indeterminate forms, maxima and minima of functions of one and two variables;

Integral Calculus

Double and triple integrals, applications of definite integrals; Fundamental theorems of integral calculus; arc lengths, areas and volumes;


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



Theorem of total probability; Axiomatic definition of probability and properties, conditional probability, multiplication rule;  Bayes’ theorem and independence of events;

Random Variables

Mathematical expectation, moments and moment generating function. Chebyshev’s inequality;
Probability mass function, probability density function and cumulative distribution functions, distribution of a function of a random variable;

Standard Distributions

Gamma, beta and normal distributions; Binomial, negative binomial, geometric, Poisson, hypergeometric, uniform, exponential, Poisson and normal approximations of a binomial distribution;

Joint Distributions

Product moments, correlation, simple linear regression; Joint, marginal and conditional distributions; Distribution of functions of random variables; Joint moment generating function; Independence of random variables;

Sampling Distribution

Chi-square, t and F distributions, and their properties;

Limit Theorems

Central limit theorem (i.i.d.with finite variance case only); Weak law of large numbers;


Sufficiency, factorization theorem; Completeness, Rao-Blackwell and Lehmann-Scheffe theorems, uniformly minimum variance unbiased estimators; Unbiasedness, consistency and efficiency of estimators, a method of moments and method of maximum likelihood; Rao-Cramer inequality. Confidence intervals for the parameters of univariate normal, two independent normals, and one parameter exponential distributions;

Testing of Hypotheses

Likelihood ratio tests for parameters of the univariate normal distribution; Basic concepts, applications of Neyman-Pearson Lemma for testing simple and composite hypotheses;

Reference books for Mathematical Statistics- IIT JAM 2019


  • Mathematical Analysis by Apostol
  • Mathematical Analysis by S.C.Malik
  • The principle of Mathematical Analysis by Rudi
  • Ordinary Differential Equation by Peter J. Collins, G.F. Simmons, M.D. Raisinghania
  • Vector Calculus by Murray R. Spiegel (Schaum’s), A.R.Vasishtha
  • Integral Calculus by F. Ayres (Schaum’s), Gorakh Prasad


  • An introduction to probability and statistics by V.K. Rohatgi
  • Introduction to Mathematical statistics by Hogg & Craig
  • Introduction to the theory of statistics by Mod & Graybill
  • Fundamentals of Mathematical statistics by S.C. Gupta & V.K. Kapoor

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