Best Mathematical Statistics Books for IIT JAM 2023

Best Mathematical Statistics Books for IIT JAM 2023

The below table contains the list of the Best Books for the IIT JAM 2023 Mathematical Statistics exam preparations.

Author/ Publication

Book’s Name

 

S.C. Gupta, V.K. Kapoor

Fundamentals of Mathematical Statistics

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Wiley

An Introduction to Probability & Statistics

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Mc Graw Hill

Introduction to the Theory of Statistics

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JBC Press

IIT-JAM Joint Admission Test for M.Sc. Mathematical Statistics 15 Years Solved Papers

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Robert V. Hogg and Craig McKean Hogg

Introduction to Mathematical Statistics

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Fundamentals of Mathematical Statistics

Fundamentals of Mathematical StatisticsKnow More

  1. Fundamentals of Mathematical Statistics (Twelfth Edition) by Sultan Chand & Sons is good for numerical competition.
  2. Don’t use for concepts, rather go for foreign authors for understanding topics.

An Introduction to Probability and Statistics

An Introduction to Probability and Statistics (Wiley Series in Probability and Statistics)Know More

  1. An Introduction to Probability and Statistics, Third Edition is an ideal reference and resource for scientists and engineers in the fields of statistics, mathematics, physics, industrial management, and engineering.

Introduction to the Theory of Statistics

Introduction to the Theory of StatisticsKnow More

  1. A comprehensive book on mathematical statistics, offering countless examples, complete derivations, and proofs.

IIT-Jam Joint Admission Test For M.Sc. Mathematical Statistics 15 Years Solved Papers (2005-2019) And 5 Model Papers

Iit-Jam Joint Admission Test For M.Sc. Mathematical Statistics 15 Years Solved Papers (2005-2019) And 5 Model PapersKnow More

  1. Well summed up previous year’s questions with detailed solutions, idle for various statistics objective exams. However few solutions to some questions aren’t elaborately explained.

Introduction to Mathematical Statistics, Global Edition

Introduction to Mathematical Statistics, Global EditionKnow More

  1. Comprehensive coverage of mathematical statistics – with a proven approach.
  2. Enhances student comprehension and retention with numerous, illustrative examples and exercises.

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To secure an excellent rank in the IIT JAM exam, one must give equal importance to other subjects too. Here is the collective list of the best books to get started with your IIT JAM preparations.

IIT-JAM 2022: Mathematical Statistics Syllabus for Preparations

The Mathematical Statistics (MS) Test Paper comprises the following topics of Mathematics (about 30% weight) and Statistics (about 70% weight).

  • Mathematics

  • Sequences of real numbers, their convergence, and limits. Cauchy sequences and their convergence. Monotonic sequences and their limits. Limits of standard sequences. Infinite series and its convergence, and divergence. Convergence of series with non-negative terms. Tests for convergence and divergence of a series. Comparison test, limit comparison test, D’Alembert’s ratio test, Cauchy’s 𝑛 𝑡ℎ root test, Cauchy’s condensation test, and integral test. Absolute convergence of series. Leibnitz’s test for the convergence of alternating series. Conditional convergence. Convergence of power series and radius of convergence.
  • Limits of functions of one real variable. Continuity and differentiability of functions of one real variable. Properties of continuous and differentiable functions of one real variable. Rolle’s theorem and Lagrange’s mean value theorems. Higher-order derivatives, Leibnitz’s rule, and its applications.
  • Taylor’s theorem with Lagrange’s and Cauchy’s form of remainders. Taylor’s and Maclaurin’s series of standard functions. Indeterminate forms and L’ Hospital’s rule. Maxima and minima of functions of one real variable, critical points, local maxima and minima, global maxima and minima, and point of inflection. Limits of functions of two real variables.
  • Continuity and differentiability of functions of two real variables. Properties of continuous and differentiable functions of two real variables. Partial differentiation and total differentiation. Leibnitz’s rule for successive differentiation. Maxima and minima of functions of two real variables. Critical points, Hessian matrix, and saddle points. Constrained optimization techniques (with Lagrange multiplier).
  • Fundamental theorems of integral calculus (single integral). Leibnitz’s rule and its applications. Differentiation under the integral sign. Improper integrals. Beta and Gamma integrals: properties and relationship between them. Double integrals. Change of order of integration. Transformation of variables. Applications of definite integrals. Arc lengths, areas, and volumes.
  • Vector spaces with the real field. Subspaces and sum of subspaces. A span of a set. Linear dependence and independence. Dimension and basis. Algebra of matrices. Standard matrices (Symmetric and Skew Symmetric matrices, Hermitian and Skew Hermitian matrices, Orthogonal and Unitary matrices, Idempotent and Nilpotent matrices).
  • Definition, properties, and applications of determinants. Evaluation of determinants using transformations. Determinant of the product of matrices. Singular and nonsingular matrices and their properties. Trace of a matrix. Adjoint and inverse of a matrix and related properties. The rank of a matrix, row-rank, column-rank, standard theorems on ranks, the rank of the sum, and the product of two matrices. Row reduction and echelon forms. Partitioning of matrices and simple properties.
  • Consistent and inconsistent system of linear equations. Properties of solutions of the system of linear equations. Use of determinants in solution to the system of linear equations. Cramer’s rule. Characteristic roots and Characteristic vectors. Properties of characteristic roots and vectors. Cayley Hamilton theorem.
  • Statistics

  • Random Experiments. Sample Space and Algebra of Events (Event space). Relative frequency and Axiomatic definitions of probability. Properties of the probability function. Addition theorem of probability function (inclusion-exclusion principle). Geometric probability. Boole’s and Bonferroni’s inequalities.
  • Conditional probability and Multiplication rule. The theorem of total probability and Bayes’ theorem. Pairwise and mutual independence of events.
  • Definition of random variables. Cumulative distribution function (c.d.f.) of a random variable. Discrete and Continuous random variables. Probability mass function (p.m.f.) and Probability density function (p.d.f.) of a random variable. Distribution (c.d.f., p.m.f., p.d.f.) of a function of a random variable using transformation of the variable and Jacobian method. Mathematical expectations and moments.
  • Mean, Median, Mode, Variance, Standard deviation, Coefficient of variation, Quantiles, Quartiles, Coefficient of Variation, and measures of Skewness and Kurtosis of a probability distribution. Moment generating function (m.g.f.), its properties, and uniqueness. Markov and Chebyshev inequalities and their applications.
  • Degenerate, Bernoulli, Binomial, Negative Binomial, Geometric, Poisson, Hypergeometric, Uniform, Exponential, Double exponential, Gamma, Beta (of the first and second type), Normal and Cauchy distributions, their properties, interrelations, and limiting (approximation) cases.
  • Definition of random vectors. Joint and marginal c.d.f.s of a random vector. Discrete and continuous type random vectors. Joint and marginal p.m.f., joint and marginal p.d.f… Conditional  c.d.f., conditional p.m.f. and conditional p.d.f.. Independence of random variables.
  • Distribution of functions of random vectors using transformation of variables and Jacobian method. Mathematical expectation of functions of random vectors. Joint moments, Covariance, and Correlation. Joint moment generating function and its properties. Uniqueness of joint m.g.f. and its applications.
  • Conditional moments, conditional expectations, and conditional variance. Additive properties of Binomial, Poisson, Negative Binomial, Gamma, and Normal Distributions using their m.g.f…
  • Multinomial distribution as a generalization of binomial distribution and its properties (moments, correlation, marginal distributions, additive property). Bivariate normal distribution, its marginal and conditional distributions, and related properties.
  • Convergence in probability, convergence in distribution, and their interrelations. Weak law of large numbers and Central Limit Theorem (i.i.d. case) and their applications.
  • Definitions of a random sample, parameter, and statistic. Sampling distribution of a statistic. Order Statistics: Definition and distribution of the 𝑟 𝑡ℎ order statistic (d.f. and p.d.f. for i.i.d. case for continuous distributions).
  • Distribution (c.d.f., p.m.f., p.d.f.) of smallest and largest order statistics (i.i.d. case for discrete as well as continuous distributions). Central Chi-square distribution: Definition and derivation of p.d.f. of central 𝜒2 distribution with 𝑛 degrees of freedom (d.f.) using m.g.f.. Properties of central 𝜒2 distribution, additive property, and limiting form of central 𝜒2 distribution.
  • Central Student’s 𝒕-distribution: Definition and derivation of p.d.f. of Central Student’s 𝑡-distribution with 𝑛 d.f., Properties and limiting form of central 𝑡-distribution. Snedecor’s Central 𝑭-distribution: Definition and derivation of p.d.f. of Snedecor’s Central 𝐹-distribution with (𝑚, 𝑛) d.f.. Properties of Central 𝐹-distribution, distribution of the reciprocal of 𝐹- distribution. Relationship between 𝑡, 𝐹, and 𝜒2 distributions.
  • Unbiasedness. Sufficiency of a statistic. Factorization theorem. Complete statistic. Consistency and relative efficiency of estimators. Uniformly minimum variance unbiased estimator (UMVUE). RaoBlackwell and Lehmann-Scheffe theorems and their applications. Cramer-Rao inequality and UMVUEs.
  •  Method of moments, method of maximum likelihood, invariance of maximum likelihood estimators. Least squares estimation and its applications in simple linear regression models.
  • Confidence intervals and confidence coefficient. Confidence intervals for the parameters of univariate normal, two independent normals, and exponential distributions.
  • Null and alternative hypotheses (simple and composite), Type-I and Type-II errors. Critical region. Level of significance, size, and power of a test, p-value. Most powerful critical regions and most powerful (MP) tests. Uniformly most powerful (UMP) tests. Neyman Pearson Lemma (without proof) and its applications to the construction of MP and UMP tests for parameters of single parameter parametric families. Likelihood ratio tests for parameters of univariate normal distribution.

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