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GATE 2021 Statistics (ST) Syllabus, Preparation Tips and Books

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Nikkil Visha

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GATE 2021 Statistics Syllabus has been revised with the addition of some new topics like Matrix Theory, Testing of Hypotheses, etc. Aspirants must go through the revised syllabus to prepare for GATE 2021 and ace it with ease. The topics in Statistics paper are based on the graduation level syllabus and does not include Engineering Mathematics topics. 

  • The weightage of the core syllabus is 85% and the remaining 15% is of General Aptitude.  Check GATE 2021 Exam Pattern
  • Candidates with ST as their first paper can only opt from MA or PH for their second paper. However, it is not mandatory that you have to appear for 2 papers. 

After qualifying GATE candidates will be to get admission in M.Tech programs offered by prestigious institutes like IITs, NIts, etc. Other than admission to M.Tech courses, candidates can also apply for  PSU recruitment through GATE  offered by various PSUs. To prepare well for the exam candidates are advised to go through the article to know more about the syllabus, exam pattern, markings scheme, some preparation tips, and important books. 

Must Read: 

GATE Syllabus of Statistics

GATE 2021 Statistics Syllabus

Below given is a detailed syllabus of GATE statics paper:

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.

Direct Link to Download GATE Statistics (ST) Syllabus PDF

Weightage of Important Topics

Weightage of Topics in GATE 2021 Statistics Syllabus

  • 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 ______________?
Important Topics Weightage
Calculus 10
Probability 15
Multivariate Analysis 12
Linear Equations 8

Check GATE Paper Analysis

Important Books for Statistics

Important Books for GATE 2021 Statistics

gate statistics
Title of the book Name of the Author/ Publication
Programmed Statistics (Question-Answers) B.L. Agarwal
Miller and Freund’s Probability and Statistics  For Engineers Pearson
Introduction to Methods of Numerical Analysis S.S. Sastry

GATE Exam Pattern of Statistics

GATE 2021 Exam Pattern of Statistics

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. 

  • 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
  • 25 questions of 1 mark each
  • 30 questions of 2 marks each 
85 marks MCQs and NATs

How to Prepare for GATE ST Paper?

GATE Preparation Tips for GATE 2021 Statistics (ST) Paper

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. 

Download GATE Previous Years Papers

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.

Must Read:  Preparation Tips from GATE Topper

6. Section Wise Preparation Tips

  • Section 1: Calculus – Statistics aspirants should prepare calculus as it is one of the vast and important topics comprising of many theorems, derivatives, and series, etc.
  • Section 2: Linear Algebra – The questions from linear algebra may be tricky and difficult to solve but GATE aspirant should prepare the syllabus to ace the exam.
  • Section 3: Probability – Probability consists of means, variables, functions, distributions, etc.
  • Section 4: Stochastic Processes – GATE Statistics consist of the study of random processes of time and random variables. The question paper is set in a tricky manner.
  • Section 5: Inference – Inference comprises of mostly Rules and Modus of inference. However, the GATE aspirant should be aware of the time and solve the questions in time.
  • Section 6: Regression Analysis – Regression, polynomial and linear regression is a time taking topics. GATE aspirants must prepare for Regression analysis to qualify for GATE exam.
  • Section 7: Multivariate Analysis – Multivariate Analysis consists of a Machine Learning Algorithm and is considered to be one of the easiest programming languages. GATE aspirants must score well in this topic if they have prepared all the topics.
  • Section 8: Design of Experiments – Design of Experiment mainly focuses on the relationship between the output of the product and the factors affecting it. The candidate should use their practical knowledge to qualify for the exam.

GATE Syllabus Of Other Papers

GATE 2021 Syllabus Of Other Papers 

Candidates who are planning to appear for GATE 2021 can check the syllabus of their respective subjects from the links provided in the table below:

Frequently Asked Questions

GATE 2021 Statistics Syllabus

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

Ans: No. There is no need to prepare for the Engineering Mathematics section if you are preparing for GATE Statistics syllabus because for this subject or discipline engineering mathematics is not the part of syllabus. You have to focus on 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 GATE Statistics syllabus? 

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? 

Ans: The weightage os 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: If there are only 2 major sections in this subject then what will be the marking scheme?

Ans: The marking scheme will remain the same. Candidates can go through the information provided in the table below: 

Section  Distribution of Marks  Total Marks
General Aptitude
  • 5 questions of 1 mark each
  • 5 questions of 2 marks each
15 marks 
  • 25 questions of 1 mark each
  • 30 questions of 2 marks each 
85 marks

Ques: Which books are best for GATE Statistics syllabus preparation? 

Ans: The best books are: 

  • Programmed Statistics (Question-Answers) – By B.L. Agarwal
  • Graduation Level books and notes should be referred by every student. 

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

GATE 2021 : 43 answered questions


Ques. Is a stipend available in PEC Chandigarh University through a valid GATE score card?

● Top Answer By Rohini Mishra on 02 May 21

Ans. To put it short, yes, you do get a stipend at the PEC Chandigarh University, but it depends on certain terms and conditions.  Getting an SGPA of at least 6.5 in the semesters is the most important condition. If it is less than required in any semester, your next stipend will not come for the next adjacent half. If you fail to do so in the 1st semester, the stipend for the second semester would be lost.  If you score SGPA more than 6.5 in the second sem, the stipend of third and fourth in the second semester combined will re-continue.  And if you fail to reach 6.5 in the second sem, the stipend of the third and fourth sem will discontinue. As there are no separate examinations for the 3rd and 4th sem to judge the eligibility of stipend.  The stipend for the first semester is received by the students without any conditions, so you need not worry about this, as this depends on your GATE score. Read more
1 Answer

Ques. What do you prefer, the GATE or the IES?

● Top Answer By Keshav Jindal on 25 Feb 21

Ans. I would prefer GATE or IES because in GATE the ratio is 10:1 whereas in IES the ratio is 300:1. This makes IES a very tough competitive exam but in GATE it is easier to get good marks and rank higher as the paper is easy and less competitive compared to IES.  The IES exam is tougher than GATE because here a candidate has to excel both in academics and personality. In GATE the questions are concept based and it is easier to solve if all the concepts are clear. Also in the GATE exam, there are 65 questions and the time limit is 3 hours but in the IES exam there are 120 questions and the time limit is 2 hours. So you get less time to solve all the questions.  After qualifying for your GATE exam with good marks, you can apply to any of the big companies with higher packages and it also opens your gate to apply for PSU.   After qualifying for your IES exam, you will get a job as an assistant executive engineer and after 3-4 years of experience, you will get promoted to executive engineer post. Then after many years of experience of like 20+ years, you will get Chief Engineer posts.Read more
1 Answer

Ques. What is the pattern for the written test for M.Tech at IIT Gandhinagar?

● Top Answer By Kumar Shiwam on 24 Feb 21

Ans. The admission for M. Tech at IIT Gandhinagar is done on the basis of academic records, written test, personal interview, and valid GATE scores. Those students who have a good academic record along with good GATE scores are not supposed to appear in the written test and personal interview.  The pattern of the written test is as follows: 10 questions of General aptitude questions consisting of logical analytical and reasoning ability and engineering mathematics are asked. 15-20 questions are asked related to basic courses in various disciplines up to the third year of an undergraduate program. The total duration of the written test is 1 hour for 80 marks. A total of 40 marks for general aptitude and 40 for basic knowledge. There is a negative marking and very basic questions are asked in the test. For branch subjects, all questions are asked related to SOM, fluid mechanics, etc.  The reservation category will get relaxation in the cut-off marks as per the norms. You will also be entitled to and fro sleeper class train tickets for the shortest route from your hometown to the institute. If you pass the test then you will attend the interview on the same day.Read more
1 Answer

Ques. What are the best coaching centres for GATE and IES in Civil Engineering?

● Top Answer By Sabeer Chalana on 23 Feb 21

Ans. There are many coaching centers throughout the country for IES and GATE coaching. However, these 2 institutes enjoy a huge reputation and recognition at the national level due to their experienced faculty and their study material quality. Made Easy: It is one of the best in the field when it comes to GATE and IES coaching. They have the best faculty teaching the subjects for the students.  Their specialty lies in their high quality and concise presentation. One of my friends enrolled in the Delhi center weekend coaching program, which he claimed to be good. Their online test series is one of the best you can opt for. They are prepared keeping the present pattern in mind. The number of students enrolled is hefty and gives you a clear picture of the competition. Some criticize that their teaching lacks depth compared to other institutes. Their courses and tests require analytical knowledge and are more than enough to crack GATE/IES exams. IES Masters: This institute is one of the best in this field and has earned respect for its excellence and quality coaching within a short span of its inception. All the major subjects for all batches are handled by Mr. Kanchan Thakur who is the director of the institute. He has a brilliant command over all the subjects in Civil engineering. The study material of this institute is best and is even recommended for those who choose civil engineering as an optional subject in UPSC exams. One small setback is that other faculties than the director are not on par when compared with the faculties of Made Easy. For the GATE Online test series, you can opt for Made easy test series, and for the IES test series you can opt for IES Masters. If you plan to join made easy to enroll in Super Talent Batch which has all top faculties teaching in this batch. For Classroom coaching for civil engineering in GATE/IES, Super talent batch can be preferred if not then IES Masters. For Postal study course, one can opt for IES masters.Read more
1 Answer

Ques. Which will be a better career for ECE engineers, IBPS SO or PSU via the GATE?

● Top Answer By Vaishnavi Agrawal on 19 Feb 21

Ans. Some of my friends work in both the departments and based on their experience, I can answer this. If you look at the position of an IBPS SO, it's that of a specialist officer. You'd technically be a network administrator of all of the intra networks of the bank. You'd be a database administrator/database manager who would have the entire intra network of that particular bank under your supervision.  Now if you look at the PSU job, you'd be someone who would be responsible for sustaining the technicalities concerning PSU. Your enquiry on which one is better entirely is up to you and where your interest lies. While some might opt for GATE which concerns their core subjects entirely, others simply might find their area of interest in networking. So, decide for yourself and choose what suits you and not the rest.Read more
1 Answer


deep mistry
Please provide topic wise weightage

Statistics paper of GATE has 9 sections:

  1. Calculus
  2. Matrix theory
  3. Probability 
  4. Stochastic Processes
  5. Estimation 
  6. Testing of Hypotheses 
  7. Non-parametric Statistics 
  8. Multivariate Analysis  
  9. Regression Analysis

Here is the weightage of different topics:

Important Topics Weightage
Calculus 10
Probability 15
Multivariate Analysis 12
Linear Equations 8
jatin sharma
Where can I get the list of the top colleges in India offering Statistics engineering course?
abdul nazir

Hi Jatin, There is no stream of Statistics Engineering available in colleges across India, however GATE score is accepted for admission to various specialised streams. To get details visit GATE 2021 participating colleges.

ankur jain
What is the usual marking scheme of GATE?
abdul nazir

Hi Ankur, From this year onwards, a new section has been added for MSQs or Multiple Select Questions. You will be awarded 1 or 2 marks depending on the section for every correct answer. Negative marking is as follows:

  • 1/3 mark will be deducted for 1 mark questions
  • 2/3 mark will be deducted for 2 mark question
  • No negative marking for MCQs and NATs

Find other details at GATE 2021 exam pattern.

Which book is good for preparation of matrix theory?
abdul nazir

Hi Swarup, There are numerous books available in the market which can help in preparation. Choose the best available one that covers the topic syllabus wise. You can check best books available subject wise at GATE recommended books.

ibashisha mukhim
Can I prepare fo statistics like that for mechanical engineering?
abdul nazir

Hi Ibashisha, You can prepare for every subject but utilizing different books available at physical store as well as e-commerce sites. Also, before the exam, you can find mock test series on the GATE official website which can be accessed by everyone. To get details visit GATE 2021 preparation tips.

Can I give the only online next year?
abdul nazir

Hi Swarup, For 2021 exam will be conducted in online mode in February 2021.As far as the next year is concerned, the details will be revealed via official notification at the right time. To get details visit GATE 2021 exam.

ibashisha mukhim
What will be the counselling procedure?
abdul nazir

Hi Ibashisha, Two process of counselling namely CCMT and COAP is conducted every year. Both are centralised admission process for admission to NITs and IITs. Seat acceptance fee is required to be paid once the seat alloted is accepted. Find other details at GATE counselling.

saurav kumar
How shall I prepare myself for the exam?
rakhisree chatterjee

Hi, GATE Preparation tips are as follows:

  1. Understanding the GATE syllabus.
  2. Collect important information and resources.
  3. Begin your preparation with dedication.
  4. Make proper revision notes.
  5. Practice tests and Quizzes.
  6. Solve the papers from previous year.
  7. Study only high quality and relevant books.

For more information, please refer, GATE Exam.

jatin sharma
How many seats are there for general candidates?
rakhisree chatterjee

Hi, Total number of seats are available in iit 10957 (approx),and 4944 seats are available for general category students. For more information, please refer, GATE Exam.

sunny pandey
What is eligibility criteria to give GATE in this subject?
rakhisree chatterjee

Hi, To appear in GATE 2021, the eligibility is relaxed from minimum 10+2+4 (appearing) to minimum 10+2+3 (appearing).  Candidates who are pursuing their-year B.Tech or UG course are also eligible to appear for GATE 2021. For more information, please refer, GATE Exam.

sadim ansari
Which college in India is best for this?

HI Sadim

Visit on our official website of Top Statistics College in India to get the top colleges across India. You will get all the other details about the colleges.

ankur jain
For how long can I use my GATE score?
common admission test

Hii Ankur, Scores of the Graduate Aptitude Test in Engineering (GATE) is valid for 3 years from the date of announcement of the GATE results. For more details Click Here

rinki mahapatra
How many times can I give GATE in a year?

Hi Rinki

The GATE Exam are held once every year. But there is no limit on the number of attempt you can give as many times you want. Visit on our official website of the GATE Exam to know all the details about the exam.