# IIT JAM Mathematical Statistics Syllabus 2020 – Get MS Syllabus PDF Here

Latest Applications Open 2020: IIT JAM Mathematics Statistic Syllabus 2020 has been Released officially by the IIT JAM 2020 authority online. Students can download the IIT JAM 2020 Syllabus into PDF format. For better preparation, Candidates can also Download other Syllabus in PDF format.

## IIT JAM Mathematics Statics Syllabus – PDF Available IIT JAM 2020 Mathematics Statics Syllabus is Available. Click here to Download PDF.

## Mathematical Statistics

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The Mathematical Statistics (MS) test paper comprises of Mathematics (40% weightage) and Statistics(60%weightage).

## Mathematics

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

## Statistics

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

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.

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. 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, the 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 normals, and one parameter exponential distributions.

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

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