Exams Prep Master

**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 |

## Important Books for Statistics

## Important Books for GATE 2021 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 |

Statistics | - 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 |

Statistics | - 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.