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**GATE 2021 Syllabus for Statistics:** Candidates can check the GATE Statistics 2021 syllabus from this page. The syllabus varies from subject to subject. GATE 2021 will be conducted for 27 subjects. The syllabus of all the subjects is different. There are 8 topics in the Statistics syllabus. These topics further have subtopics under them. The syllabus of all the subject papers is available on the official website of GATE. Candidates can check the entire syllabus for Statistics from this page.

## GATE 2021 Syllabus for Statistics

The syllabus for the GATE 2021 Statistics paper includes topics like Calculus, Linear Algebra, Probability, Stochastic Processes, Inferences, Regression Analysis, Multivariate Analysis, and Design of experiments. There are various subtopics under these topics. Candidates can check the complete syllabus from below –

**Calculus:** Finite, countable and uncountable sets; Real number system as a complete ordered field, Archimedean property; Sequences of real numbers, the convergence of sequences, bounded sequences, monotonic sequences, Cauchy criterion for convergence; Series of real numbers, convergence, tests of convergence, alternating series, absolute and conditional convergence; Power series and radius of convergence; Functions of a real variable: Limit, continuity, monotone functions, uniform continuity, differentiability, Rolle’s theorem, mean value theorems, Taylor’s theorem, L’ Hospital rules, maxima and minima, Riemann integration and its properties, improper integrals; Functions of several real variables: Limit, continuity, partial derivatives,

directional derivatives, gradient, Taylor’s theorem, total derivative, maxima and minima, saddle the point, method of Lagrange multipliers, double and triple integrals, and their applications.

**Matrix Theory: **Subspaces of and, span, linear independence, basis, and dimension, row space and column space of a matrix, rank and nullity, row reduced echelon form, trace, and determinant, the inverse of a matrix, systems of linear equations; Inner products in and , Gram-Schmidt orthonormalization; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal, unitary matrices and their eigenvalues, change of basis matrix, equivalence and similarity, diagonalizability, positive definite and positive semi-definite matrices and their properties, quadratic forms, singular value decomposition.

**Probability:** Axiomatic definition of probability, properties of probability function, conditional probability, Bayes’ theorem, independence of events; Random variables and their distributions, distribution function, probability mass function, probability density function and their properties,

expectation, moments and moment generating function, quantiles, distribution of functions of a random variable, Chebyshev, Markov and Jensen inequalities.

**Standard discrete and continuous univariate distributions:** Bernoulli, binomial, geometric, negative binomial, hypergeometric, discrete uniform, Poisson, continuous uniform, exponential, gamma, beta, Weibull, normal. Jointly distributed random variables and their distribution functions, probability mass function, probability density function, and their properties, marginal and conditional distributions, conditional expectation and moments, product moments, simple correlation coefficient, joint moment generating function, independence of random variables, functions of random vector and their distributions, distributions of order statistics, joint and marginal distributions of order statistics; multinomial distribution, bivariate normal distribution, sampling distributions: central, chi-square, central t, and central F distributions. Convergence in distribution, convergence in probability, convergence almost surely, convergence in r-the mean and their inter-relations, Slutsky’s lemma, Borel-Cantelli lemma; weak and strong laws of large numbers; central limit theorem for i.i.d. random variables, delta method.

**Stochastic Processes: **Markov chains with finite and countable state space, classification of states, limiting behavior of n-step transition probabilities, stationary distribution, Poisson process, birth-and-death process, pure-birth process, pure-death process, Brownian motion and

its basic properties.

**Estimation:** Sufficiency, minimal sufficiency, factorization theorem, completeness, completeness of exponential families, ancillary statistic, Basu’s theorem and its applications, unbiased estimation, uniformly minimum variance unbiased estimation, Rao-Blackwell theorem, Lehmann-Scheffe theorem, Cramer-Rao inequality, consistent estimators, method of moments estimators, method of maximum likelihood estimators and their properties; Interval estimation: pivotal quantities and confidence intervals based on them, coverage probability.

**Testing of Hypotheses: **Neyman-Pearson lemma, most powerful tests, monotone likelihood ratio (MLR) property, uniformly most powerful tests, uniformly most powerful tests for families having MLR property, uniformly most powerful unbiased tests, uniformly most powerful unbiased tests

for exponential families, likelihood ratio tests, large sample tests. Non-parametric Statistics: Empirical distribution function and its properties, the goodness of fit tests, chi-square test, Kolmogorov-Smirnov test, sign test, Wilcoxon signed-rank test, Mann-Whitney U-test, rank correlation coefficients of Spearman and Kendall.

**Multivariate Analysis:** Multivariate normal distribution: properties, conditional and marginal distributions, maximum likelihood estimation of mean vector and dispersion matrix, Hotelling’s T2 test, Wishart distribution and its basic properties, multiple and partial correlation coefficients

and their basic properties.

**Regression Analysis:** Simple and multiple linear regression, R2 and adjusted R2 and their applications, distributions of quadratic forms of random vectors: Fisher-Cochran theorem, Gauss-Markov theorem, tests for regression coefficients, confidence intervals.

### GATE 2021 General Aptitude Syllabus

The syllabus for General Aptitude is the same in all the GATE 2021 subject papers. A total of 10 questions come in this section. Out of these 10 questions, 5 are of 1 mark each and the other 5 are of 2 marks each. Under General Aptitude, there are two parts – Verbal Ability and Numerical Ability. The syllabus for General Aptitude is given below.

**Verbal Ability:** English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction. **Numerical Ability:** Numerical computation, numerical estimation, numerical reasoning and data interpretation.

### GATE 2021 Statistics Exam Pattern

Before you start the preparation for Statistics, you must know the exam pattern and marking scheme of GATE Statistics 2021. Exam pattern tells you the details regarding the pattern of the exam including, mode of conduct, duration, etc. Marking scheme is as important as the exam pattern. The scheme informs you about the total marks of the exam and how marks are given for specific questions. To know the exam pattern and the marking scheme in detail, read below.

Section | Distribution of Marks | Total Marks | Types of questions |

GA | 5 questions of 1 mark each 5 questions of 2 marks each | 15 marks | MCQs |

ST- Subject-Based | 25 questions of 1 mark each 30 questions of 2 marks each | 85 marks | MCQs and NATs |

**Mode:** Online, Computer Based Test

**Duration:** 3 hours

**Types of questions:** MCQs and NATs (Numerical Answer Type)

**No./Name of sections:** 3 Sections – General Aptitude, Mathematics and Subject-based

**No. of questions:** 65 questions

**Total marks:** 100 marks

**Negative marking:** Only for MCQs

**Marking scheme**:

Type of question | Negative marking for wrong answer | Marking for correct answer |

MCQs | ⅓ for 1 mark questions⅔ for 2 marks questions | 1 or 2 marks |

NATs | No negative marking | 1 or 2 marks |

### How to Prepare for Statistics?

Candidates must prepare for statistics subject in GATE 2021 strategically. The subject is more inclined towards mathematics and numericals. You should practice a lot for this particular subject. You should complete the syllabus on time with a sufficient amount of practice. Then move on to solving questions papers of past years and mock tests. Also, practice from online test series. Your preparation should be thorough. We have put together a few tips that will help you prepare better for the GATE 2021. You can check them out below.

**Start easy**

It is always better to start your preparation from the easy topics. It will give you the confidence to move forward in your preparation. This way you can cross those topics from the syllabus and you will be left with the difficult topics only. These topics require more attention and hard work. Separate them in medium and hard difficulty levels. Complete the medium topics before hard ones. This way you will cover most of the syllabus and including the important topics.

**Focus on practicing**

Statistics is all about quantitative aptitude. You focus should be on solving more and more numericals. Try to practice numericals of all difficulty level. This will help you big time in the exam. Don’t shy away from hard topics or problems that are difficult to solve. Also, practice quick mental calculations. This will save a lot of your time in the exam. Your mind will be alert and sharp and it will not be difficult to solve questions in a matter of minutes.

**Complete the syllabus**

Completing the syllabus is very important. Even if you start your preparation right at the moment, you will still have enough time to cover the entire syllabus in a few months and still have a month for just revision. The subject is not foreign to many students as they have already studied it in school. Make use of that prior knowledge. Try to cover it all in about 4-5 months. It is enough to complete the syllabus if you prepare smartly.

**Practice Mock tests **

Mock tests are an important part of your preparation. You should take weekly and subject-wise mock tests. If possible take monthly mock tests as well. These regular mock tests will help you in keeping your preparation in check. After every test analyze your performance. Identify your weak areas and work on them accordingly. Analysis is an important step. Without it, your mock test practice is of no use. So make sure that you analyze each one of them properly.

**Solve Previous years question papers**

Along with mock tests, you should also solve previous year question papers. Pick up the last 5-6 years question papers and start solving them. Observe the trend of questions that have been followed over the past years. Practice time management while solving papers. Prepare a strategy of how to attend the paper and in what sequence.

**Do revision**

Revision should be done after every topic is completed. Make it a habit so that you don’t slack while revising. You can also prepare running notes. They will come in handy in the last month when you will be revising. Revising from notes will also be easier. In case you don’t remember some topics even after reading your notes then you can refer to the study material.

### GATE Statistics Books for Preparation

Prepare for your GATE 2021 from the best study material only. Your study material should be of good quality. Pick books from renowned publications and authors. The quality of your study material reflects the quality of your GATE preparation. Especially if you are doing self-preparation, then you must invest in good quality books and notes. If you are still having trouble finding the right study material, then you can refer to the list of books we have given below.

Title of the book | Name of the Author/ Publication | Link to buy |

Programmed Statistics (Question-Answers) | B.L. Agarwal | LINK |

Miller and Freund’s Probability and Statistics For Engineers | Pearson | LINK |

### What is Statistics?

Statistics is one of the mathematics branches that includes working with data collection, organization, analysis, interpretation and presentation. In Engineering Statistics is mixed with engineering through scientific methods for analyzing data. It involves data related to manufacturing processes including component dimensions, tolerances, types of materials, and fabrication process control. For engineering analysis, various methods are used that are displayed as histograms to visualize the data.

### GATE 2021 Preparation FAQs

**Q1. Which books should I prepare for Statistics?****Ans.** You can prepare from the books we have suggested in this article.

**Q2. Can I leave some topics in the syllabus? ****Ans.** You should prepare the whole syllabus. If you don’t have enough time then you can do the important topics and solve mock tests.

**Q3. How many months are needed to complete the syllabus?****Ans. **Ideally your syllabus should be completed in about 4-5 months. The last/6th month should be for revision.