JAM Mathematical Statistics Syllabus 2020

For Mathematics:-

Sequences and Series - Comparison, Root and Ratio Tests for Convergence of Series of Real Numbers, Convergence of Sequences of Real Numbers.

Differential Calculus - Limits, Continuity and Differentiability of Functions of One and Two Variables. Rolle's Theorem, Mean Value Theorems, Indeterminate Forms, Taylor's Theorem, Maxima and Minima of Functions of One and Two Variables.

Integral Calculus - Fundamental Theorems of Integral Calculus, Applications of Definite Integrals, Arc Lengths, Double and Triple Integrals, Areas and Volumes.

Matrices - Rank, Inverse of a Matrix, Systems of Linear Equations, Eigenvalues and Eigenvectors, Linear Transformations, Symmetric, Cayley-Hamilton Theorem, Skew-Symmetric and Orthogonal Matrices.

For Statistics:-

Probability - Axiomatic Definition of Probability and Properties, Multiplication Rule, Theorem of Total Probability, Conditional probability, Bayes' Theorem and Independence of Events

Random Variables - Probability Mass Function, Distribution of a Function of a Random Variable, Mathematical Expectation, Probability Density Function and Cumulative Distribution Functions, Moments and Moment Generating Function, Chebyshev's Inequality.

Standard Distributions - Geometric, Binomial, Negative Binomial, Poisson, Hypergeometric, Uniform, Beta and Normal Distributions, Exponential, Gamma. 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, Correlation, Simple Linear Regression, Product Moments, Independence of Random Variables.

Sampling distributions - 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, Method of Moments and Method of Maximum Likelihood, Consistency and Efficiency of Estimators. Sufficiency, Factorization Theorem, Rao-Blackwell and Lehmann-Scheffe Theorems, Completeness, Uniformly Minimum Variance Unbiased Estimators, Confidence Intervals for the Parameters of Univariate Normal, Two Independent Normal, and one Parameter Exponential Distributions. Rao-Cramer Inequality

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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