*Go through important IIT JAM Mathematical Statistics books that aspirants should read for important Mathematics and Statistics topics of IIT JAM 2022.*

IIT JAM 2022 will be held on February 13. On the exam day, IIT Roorkee will conduct the IIT JAM paper for the Mathematical Statistics course in Session-I, that is, from 9:30 am to 12:30 pm. Questions in the IIT JAM Mathematical Statistics paper is divided into two parts. The first part comprises questions from Mathematics. The weightage of this section in the exam is 40 per cent. The second part has questions from Statistics and the weightage of this section is 60 per cent.

Candidates are advised to know the IIT JAM exam pattern and syllabus thoroughly when they plan to take this popular Science entrance exam. This is necessary because there is negative marking in the exam and candidates should know the marking scheme of the exam to ensure that they score the highest marks in the exam.

Apart from this, for IIT JAM preparation, candidates should have a strategy in place. Thus, after completing the JAM syllabus 2021, candidates should practise as many question papers and mock tests for the exam as they can get their hands on.

## Topics to Study in IIT JAM Mathematical Statistics

Table of Contents

Aspirants can go through important topics that they should study to secure good marks in the IIT JAM exam for Mathematical Statistics below:

Important Topics in Mathematics | |
---|---|

Sequences and Series | Differential Calculus |

Integral Calculus | Matrices |

Important Topics in Statistics | |

Probability | Random Variables |

Standard Distributions | Joint Distributions |

Sampling Distributions | Limit Theorems |

Estimation | Testing of Hypotheses |

**IIT JAM MATHEMATICAL STATISTICS (MS) 2022 latest** **SYLLABUS**

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

**》Mathematics**

**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.

**》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. 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, 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.

## Best Books to Study for IIT JAM Mathematical Statistics Preparation 2022

Aspirants can go through topic-wise books that they can refer to when they are preparing for the IIT JAM Mathematical Statistics paper below.

### IIT JAM Mathematical Statistics Books to Read for Mathematics

Books that aspirants should consider reading for topics in the Mathematics section of the exam are mentioned below:

Name of the Book | Author |
---|---|

Mathematical Analysis | S.C. Malik |

Mathematical Analysis | Apostol |

Principle of Mathematical Analysis | Rudi |

Schaum’s Outlines Integral Calculus | Frank Ayres, Elliott Mendelson |

Integral Calculus | Dr Gorakh Prasad |

Vector Analysis: Schaum’s Outlines Series | Murray Spiegel, Seymour Lipschutz, Dennis Spellman |

Geometry and Vector Calculus | A.R. Vasishtha |

Ordinary Differential Equation | Peter J. Collins, G.F. Simmons, M.D. Raisinghania |

### IIT JAM Mathematical Statistics Books to Read for Statistics

Books that aspirants should consider reading for topics in the Statistics section of the exam are mentioned below:

Name of the Book | Author |
---|---|

Introduction to the Theory of Statistics | Alexander Mood, Franklin Graybill, Duane Boes |

An Introduction to Probability and Statistics | V.K. Rohatgi |

Apart from the above-mentioned books, aspirants should also go through the books mentioned below to prepare for IIT JAM exam for Mathematical Statistics 2022.

Name of the Book | Author |
---|---|

IIT JAM: MSc Mathematical Statistics | Anand Kumar |

Complete Resource Manual MSc Mathematics | Suraj Singh |

Fundamental of Mathematical Statistics | S.C. Gupta & V.K. Kapoor |

Introduction to Mathematical Statistics | Robert V. Hogg and Craig Mckean Hogg |