## IIT JAM(MS) SYLLABUS

IIT JAM Syllabus for Mathematical Statistics (MS)

The JAM test paper for Mathematical Statistics consists of two subjects which are Mathematics and Statistics. The weightage given to Mathematics is 40 percent and to Statistics is 60 percent. Aspirants can go through detailed IIT JAM Mathematical Statistics syllabus here. Find out the important topics for Mathematical Statistics course below:

IIT JAM Mathematics 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, the inverse of a matrix. Systems of linear equations. Linear transformations, eigenvalues, and eigenvectors. CayleyHamilton theorem, symmetric, skew-symmetric, and orthogonal matrices.

IIT JAM Statistics Syllabus

• Probability: mass function, probability density function and cumulative distribution functions, distribution of a function of a random variable. Probability: Axiomatic definition of probability and properties, conditional probability, multiplication rule. The theorem of total probability. Bayes’ theorem and independence of events.

• Random Variables: Mathematical expectation, moments and moment generating function. Chebyshev's inequality.

•  Joint Distributions: Joint, marginal and conditional distributions. Distribution of functions of random variables. Joint moment generating function. 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).

• Estimation: Unbiasedness, consistency and efficiency of estimators, method of moments and method of maximum likelihood. Sufficiency, factorization theorem. Completeness, RaoBlackwell 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.

• Testing of Hypotheses: Basic concepts, applications of NeymanPearson Lemma for testing simple and composite hypotheses. Likelihood ratio tests for parameters of univariate normal distribution