The conducting body has prescribed a particular set of syllabus for JAM 2020. The exam is conducted for 6 subjects in online mode. Indian Institute of Technology, Kanpur will conduct Joint Admission Test for M.Sc. (JAM) 2020. The exam is conducted for admission in M.Sc. (Two Years), Joint M.Sc.-Ph.D., M.Sc.-Ph.D. Dual Degree, and other Post-Bachelor Degree Programmes. The exam is conducted for 3 hours in online mode. Candidates can read the full article for more information about JAM 2020 syllabus

## JAM Syllabus for Mathematical Statistics (MS)

There are 12 topics in Mathematical Statistics. The exam is conducted for 6 papers but the candidate can appear for either one for 2 subjects. Candidate can appear in two test papers if they are not scheduled in the same session.

### Topics included in JAM Mathematical Statistics (MS)

Candidates can check below the topics included in JAM Mathematical Statistics 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 the 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.

### JAM Previous year Question paper

Previous year question papers will help the candidate to understand how much time should be dedicated to which section. It is beneficial for candidates to practise from previous year question paper as the candidate can understand the exam pattern, what type of questions are there in the paper, how much marks is allotted to which section. The previous year question papers are present on the official website of JAM.

**Candidates can download the previous year question paper from ****here****.**

### Exam Pattern for JAM 2020

Candidates can check below the exam pattern for JAM 2020.

**Exam Type –**Objective type test**Number of questions –**60**Time duration –**3 hours**Total Marks –**100

Section | Type of Question | Number of questions |

Section A | MCQ | 10 of 1 marks each20 of 2 marks each |

Section B | MSQ | 10 of 2 marks each |

Section C | NAT | 10 of 1 marks each10 of 2 marks each |

**Marking Pattern**

For Section A

- For 1 mark question -⅓ deducted
- For 2 mark question -⅔ deducted

**No negative marking in Section B and C**

### Books to cover JAM Mathematical Statistics (MS) Syllabus

Candidates can check below some books for Mathematical Statistics preparation.

- IIT JAM Mathematical Statistics – Anand Kumar
- Complete Resource Manual M.Sc. Mathematics – Suraj Singh
- Fundamental of Mathematical Statistics – S.C Gupta and V.K Kapoor
- Introduction to Mathematical Statistics – Hogg and Craig
- Introduction to the theory of Statistics – Mod and Graybill
- An introduction to probability and Statistics – V.K Rohatgi

## About JAM 2020

The examination is open to all Indian and Foreign candidates. The exam is conducted for admission in M.Sc. (Two Years), Joint M.Sc.-Ph.D., M.Sc.-Ph.D. Dual Degree, and other Post-Bachelor Degree Programmes. JAM 2020 will have six Test Papers, namely, Biotechnology (BT), Chemistry (CY), Geology (GG), Mathematics (MA), Mathematical Statistics (MS) and Physics (PH). It is a 3 hour Computer based online exam.