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**IIT JAM 2018 Mathematical Statistics Syllabus **

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

**JAM 2018 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, inverse of a matrix. systems of linear equations. Linear transformations, eigenvalues and eigenvectors. Cayley – Hamilton theorem, symmetric, skew – symmetric and orthogonal matrices.

**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.

**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. 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, 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.

**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.

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