# IIT JAM Mathematical Statistics Syllabus 2021 – Get MS Syllabus PDF Here

**IIT JAM Mathematics Statistic Syllabus 2021** will be **released officially** by the **IIT JAM 2021** authority **online.**

Students can download the **IIT JAM 2021 Syllabus** into PDF format. For better preparation, Candidates can also Download other **Syllabus** in **PDF** format.

The **IIT JAM** is known as the India Institute of Technology and the Indian Institute of Science may offer the **Joint Admission Test for Masters of Science and Technology**

## Mathematical Statistics

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

## Mathematics

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**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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