# GATE Statistics Syllabus 2022: Important Topics, Weightage, Exam Pattern, QuestionPapers, and Books

Content Curator | Updated On - Oct 7, 2021

GATE Statistics Syllabus 2022 consists of 9 different sections, Calculus, Matrix Theory, Probability, Stochastic process, Estimation, Testing of hypothesis, Nonparametric Statistics, Multivariate Analysis and Regression Analysis. The syllabus includes all the major topics of the graduate level but does not include Engineering Mathematics as a topic.The most important Topic in the GATE Statistics Syllabus is Probability as it comprises almost 20% of the total weightage in the GATE Paper. The weightage of the core syllabus is 85% and the remaining 15% is of General Aptitude. Check GATE 2022 Exam Pattern

GATE 2022 would be conducted by IIT Kharagpur and is expected in the month of February 2022. GATE 2022 Statistical Paper would have 65 questions totalling 100 marks.Candidates with Statistics (ST) as their first paper can only opt one paper from either Mathematics (MA) or Physics (PH) as their second paper. However, it is not mandatory that you have to appear for 2 papers

GATE ST Syllabus

## GATE Statistics Syllabus 2022

GATE Statistics Syllabus 2022 consists of 9 different sections, they are : Calculus, Matrix Theory, Probability, Stochastic process, Estimation, Testing of hypothesis, Non parametric Statistics, Multivariate Analysis and Regression Analysis. The detailed syllabus for which is given below-

### Section 1: Calculus

• Finite, countable and uncountable sets; Real number system as a complete ordered field, Archimedean property; Sequences of real numbers, 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 point, method of Lagrange multipliers, double and triple integrals and their applications.

### Section 2: Matrix Theory

• Subspaces of Rnn and Cnn, span, linear independence, basis and dimension, row space and column space of a matrix, rank and nullity, row reduced echelon form, trace and determinant, inverse of a matrix, systems of linear equations; Inner products in Rnn and Cnn, 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.

### Section 3: 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-th 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.

### Section 4: Stochastic Processes

• Markov chains with finite and countable state space, classification of states, limiting behaviour 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.

### Section 5: 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.

### Section 6: 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.

### Section 7: Non-parametric Statistics

• Empirical distribution function and its properties, 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.

### Section 8: 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.

### Section 9: 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.

Check:

GATE ST Weightage

## GATE Statistics Syllabus 2022 : Weightage of Important Topics

By the Previous Year GATE Chemistry Paper Analysis, the general trend in the GATE Statistics exam in terms of the weightage of the different subjects is given below.

Important Topics Weightage in terms of Question asked
Calculus 15
Probability 20
Multivariate Analysis 10
Linear Equations 15
Matrix Theory  8
Estimation  8
Stochastic process 8
Testing of Hypotheses 8
Regression Analysis 8

GATE ST Exam Pattern

## GATE Statistics Syllabus 2022: Exam Pattern

GATE marks are distributed according to the guidelines formulated by the conducting body of the exam. While preparing for GATE ST, candidates should have good knowledge about GATE Exam Pattern.The salient features of the Exam pattern are as following -  Read More about GATE Exam Pattern

• Mode of Examination: Online
• Duration of Exam: 3 hours
• Types of questions: MCQs and NATs (Numerical Answer Type)
• Total Sections: 3 Sections – General Aptitude, Mathematics and Subject-based
• No. of questions: 65 questions
• Total marks: 100 marks
• Negative marking: Only for MCQs
Section  Distribution of Marks Total Marks Types of questions
General Aptitude
• 5 questions of 1 mark each
• 5 questions of 2 marks each
15 marks  MCQs
Statistics
• 25 questions of 1 mark each
• 30 questions of 2 marks each
85 marks MCQs and NATs

### GATE 2022 Marking scheme:

• Total Marks: 100 marks
• Negative Marking: For MCQs only
Type of question Negative marking for wrong answer
MCQs ⅓ for 1 mark questions ⅔ for 2 marks questions
NATs No negative marking

GATE ST Preparation

## GATE Statistics Syllabus 2022: Preparation

The GATE Statistics includes a lot of lengthy and complex calculations, so here are a few reference books, previous year papers and sample questions to help a student. Students can also refer to GATE Preparation Tips to learn more about GATE Preparation Strategy.

#### 1. Practice Papers and Mock Tests

• Practice Papers: With the help of papers of previous years or model test papers candidates can get an idea about the weightage of the questions, type of questions, important topics, etc. Candidates are advised to solve the questions from previous years' papers after completion of each topic.
• Mock Tests: Mock Tests are online tests and they give the feel of the real exam. you can check your level of preparation, accuracy, and speed while attempting the mock test. Candidates are suggested to go for the mock test only after the completion of whole syllabus.

#### 2. Video Lectures

Candidates can attend online video lectures from experts. This will help you in clearing the concepts. You can fix a day in your time table to watch a few video lectures. No need to do it on a regular basis.

#### 3. Daily Revision & Making Notes

• Daily revision is very helpful in remembering all the important points or formulas.
• Candidates should devote 2-3 hours daily for revision of all the important topics that they have covered.
• To make revisions easy, you can make notes for revision.
• These notes should have all the important tricks, tips, formulas, etc.

#### 4. Follow a Time Table

• Candidates following a time table can easily cover all the topics.
• Time Table provide a routine to candidates.
Time Table Activities
5:00 AM to 8:00 AM Revision from Notes
8:00 AM to 10:00 AM Take a Break
10:00 AM to 1:00 PM Start a New Topic
1:00 PM to 5:00 PM Take a Break
6:00 PM to 9:00 PM Complete the topic/ Go through the same topic again
10:00 PM Write down important points covered in the day and sleep early

#### 5. Do’s and Don’ts of Preparation

• Do not overdo with preparations. Take frequent breaks as well.
• Initially, when you will begin your preparations, you won’t be able to score much in mock tests or solve many questions correctly. Do not get de-motivated because of it. It is just the indication of the level you are at. Analyze your weak areas and master them.
• Do not compare your progress & preparation with your classmates or friends. You have your own skills, strategies, plans and speed. Comparing will never help. So just focus on improving yourself.
• Do not lose track of your goal. It is very important to stay focused on your goal till the end. You may have a bad day, but do not lose track.
• Do not compromise your health. Health is very important. So, take proper care of yourself.

### Important Books for GATE Statistics Syllabus 2022

Title of the book Name of the Author/ Publication
Miller and Freund’s Probability and Statistics For Engineers Pearson
Introduction to Methods of Numerical Analysis S.S. Sastry
An Introduction to Multivariate Statistical Analysis T.W. Anderson
Matrix Theory  Joel Nick Franklin
Stochastic Processes Seldon M. Ross
Theory of Estimation Erich L. Lehmann

Check Out:

GATE ST Question Papers

### GATE Statistics Previous Year Question Papers and Answer Keys

GATE conducting authorities release the Question paper for the year and the respective GATE Answer Key for all 27 papers after all the exams for the year have been concluded.Going through previous years GATE question paper gives an insight into the important topics from GATE Syllabus. Given below are the links to download the previous year GATE Question Paper from 2021, 2020 and 2019

Year GATE Question paper Answer Key

### GATE Statistics Syllabus 2022: Sample Questions

• Sample Question 1: A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes is _____________?
• Sample Question 2: Let A be a 6 × 6 complex matrix with A 3 ≠ 0 and A 4 = 0. Then the number of Jordan blocks of A is ___________?
• Sample Question 3: Let X1, ... , Xn be a random sample drawn from a population with probability density function f(x; θ) = θx θ−1, 0 ≤ x ≤ 1, θ > 0. Then the maximum likelihood estimator of θ is ______________?

## GATE 2022 Syllabus Of Other Subjects

Tabulated below is the syllabus of other subjects of GATE 2022 that students may refer to.

## GATE Statistics Syllabus 2022 : FAQ

Ques. Do I need to prepare for the Engineering Mathematics section while preparing for the GATE Statistics syllabus 2022?

Ans: No. There is no need to prepare for the Engineering Mathematics section if you are preparing for the GATE Statistics syllabus 2022 because engineering mathematics is not part of the Statistics syllabus. Although, you have to focus on the general aptitude section which is common for all the disciplines of GATE and core subject syllabus only.

Ques. What are the major topics that I need to cover in the GATE Statistics syllabus 2022?

Ans: The major topics that you need to cover in GATE Statistics syllabus are mentioned below:

• General Aptitude
• Calculus
• Linear Algebra
• Probability
• Stochastic Processes
• Inference
• Regression Analysis
• Multivariate Analysis
• Design of Experiments

Ques. What will be the weightage of important sections in GATE Statistics syllabus 2022?

Ans: The weightage of section is mentioned below:

• General Aptitude – 15%
• Statistics Syllabus (All Topics) – 85%

This means out of 65 questions 10 questions will be asked from General aptitude and remaining 55 questions from core subject syllabus.

Ques. Which books are best for GATE Statistics syllabus 2022?

Ans: The best books are:

Title of the book Name of the Author/ Publication
Miller and Freund’s Probability and Statistics For Engineers Pearson
Introduction to Methods of Numerical Analysis S.S. Sastry
An Introduction to Multivariate Statistical Analysis T.W. Anderson
Matrix Theory  Joel Nick Franklin
Stochastic Processes Seldon M. Ross
Theory of Estimation Erich L. Lehmann

Ques. Which is the most important topic in the GATE Statistics Syllabus 2022?

Ans. The most important Topic in the GATE Statistics Syllabus is Probability as it comprises almost 20% of the total weightage. Calculus is the next important topic with 15% weightage.

Ques. What is the GATE 2022 Statistics Exam Pattern?

Ans. The GATE Statistics Exam Pattern is as follows:

Section  Distribution of Marks Total Marks Types of questions
General Aptitude
• 5 questions of 1 mark each
• 5 questions of 2 marks each
15 marks  MCQs
Statistics
• 25 questions of 1 mark each
• 30 questions of 2 marks each
85 marks MCQs and NATs

Ques. Is there any negative marking for GATE 2021 numerical answer type questions in GATE Statistics Syllabus 2022?

Ans. No, there is no negative marking for numerical answer type questions asked in GATE Statistics Syllabus.MCQs do have negative marking as ⅓ for each 1 Marks question and ⅔ for each wrong 3 marks question

Ques. What is the negative marking for a wrong answer for the 1-mark question in GATE 2021?

Ans. A candidate will lose ⅓ marks for every wrong answer to the 1-mark question in GATE 2021.

Ques. What is the subject code for GATE Statistics?

Ans. The paper code for GATE Statistics is ST. Candidates with Statistics (ST) as their first paper can only opt for one paper from either Mathematics (MA) or Physics (PH) as their second paper. However, it is not mandatory that you have to appear for 2 papers

Ques. What are the sub-topics included in the Matrix Theory of the GATE Statistics Syllabus 2022?

Ans. The sub-topics included in the Matrix Theory of the GATE Statistics Syllabus 2022 are:

• Subspaces of Rnn and Cnn, span, linear independence, basis and dimension, row space and column space of a matrix, rank and nullity, row reduced echelon form, trace and determinant, inverse of a matrix, systems of linear equations; Inner products in Rnn and Cnn, 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.

*The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College.

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