JAM Mathematical Statistics Syllabus 2023
JAM Mathematical Statistics Syllabus 2023
JAM Mathematical Statistics Syllabus 2023 : Comparison, Root as well as Ratio Tests for Convergence of Series of Real Numbers, Convergence of Sequences of Real Numbers, Limits, Continuity,along with Differentiability of Functions of One along with Two Variables.
Rolle’s Theorem, Mean Value Theorems, Indeterminate Forms, Taylor’s Theorem, Maxima as well as Minima of Functions of One and Two Variables.
Fundamental Theorems of Integral Calculus, Applications of Definite Integrals, Arc Lengths, Double as well as Triple Integrals, Areas, and Volumes.
Rank, Inverse of a Matrix, Systems of Linear Equations, Eigenvalues as well as Eigenvectors, Linear Transformations, Symmetric, Cayley-Hamilton Theorem, Skew-Symmetric, and Orthogonal Matrices.
Axiomatic Definition of Probability and Properties, Multiplication Rule, Theorem of Total Probability, Conditional probability, Bayes’ Theorem and Independence of Events, Probability Mass Function, Distribution of a Function of a Random Variable,
Mathematical Expectation, Probability Density Function, along with Cumulative Distribution Functions, Moments and Moment Generating Function, Chebyshev’s Inequality. Geometric, Binomial, Negative Binomial, Poisson, Hypergeometric, Uniform, Beta along with Normal Distributions, Exponential, Gamma.
Poisson and Normal Approximations of a Binomial Distribution. Joint, Marginal, along with Conditional Distributions, Distribution of Functions of Random Variables, Joint Moment Generating Function, Correlation, Simple Linear Regression, Product Moments, Independence of Random Variables.
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Chi-Square, T as well as F Distributions and their Properties Weak Law of Large Numbers, Central Limit Theorem (i.i.d.with Finite Variance Case only) Unbiasedness, Method of Moments as well as Method of Maximum Likelihood, Consistency and Efficiency of Estimators.
Sufficiency, Factorization Theorem, Rao-Blackwell, along with Lehmann-Scheffe Theorems, Completeness, Uniformly Minimum Variance Unbiased Estimators, Confidence Intervals for the Parameters of Univariate Normal, Two Independent Normal, along with one Parameter Exponential Distributions.
Rao-Cramer Inequality, Basic Concepts, Applications of Neyman-Pearson Lemma for Testing Simple as well as Composite Hypotheses, Likelihood Ratio Tests for Parameters of Univariate Normal Distribution.
This is it in JAM Mathematical Statistics Syllabus 2023 Also Check JAM Biotechnology Syllabus 2023 & JAM Physics Syllabus 2023 & JAM Mathematics Syllabus 2023 & JAM Chemistry Syllabus 2023 .
