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TN TRB Assistant Professor Statistics Free Mock Test
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TN TRB Assistant Professor Statistics Syllabus 2026, Exam Pattern
TN TRB Assistant Professor Statistics Syllabus 2026, Exam Pattern, Exam Date 2026
Detail Information about TN TRB has published notification 2026 for the Notification of Assistant Professor Statistics. Those Candidates who are Interested to the following vacancy and completed all Eligibility Criteria can read the Notification & Apply Online. In this page we provide the Complete Syllabus of this Recruitment Exam with Latest Update Exam Pattern and the Exam Date also.
TN TRB Assistant Professor Syllabus 2026 - Overview
TN TRB Assistant Professor Statistics Syllabus 2026
Paper-I Syllabus :-
Part A: Compulsory Tamil
1. Reading Comprehension
2. Fillers
3. Cloze test
4. Tenses
5. Adjectives
6. Adverbs
7. Prepositions
8. Sentence Completion
9. Paragraph Completion
10. Antonym and synonym
11. Grammatical Error based question
Part B: Concerned Subject - Statistics :
Unit 1
Real Analysis: Set theory, Bolzano Weierstrass theorem, Sequences and Series, Convergence, Sequences and Series of functions, Uniform Continuity, Differentiability, Riemann sums and Riemann Integral.
Linear Algebra: Vector Spaces, Subspaces, Linear Dependence, Basis, Dimension, Algebra of Linear Transformations, Algebra of Matrices, Rank and Determinant of Matrices, Linear Equations, Eigenvalues, Eigenvectors, Cayley-Hamilton theorem. Change of basis, Canonical forms, Diagonal forms, Triangular forms, Jordan forms. Inner Product Spaces, Orthonormal basis. Quadratic forms, Reduction and Classification of Quadratic forms.
Measure Theory: Measurable spaces, Extension of measure, Signed measure, Jordan-Hahn decomposition theorems. Lebesgue measure, Metric Spaces, Convergence, Continuity, Compactness, Connectedness, Monotone Convergence theorem, Fatou’s Lemma, Dominated Convergence theorem, Absolute Continuity of two measures, Radon-Nykodym theorem, Product measures, Fubini’s theorem.
Unit 2
Probability Theory: Sample Space, Discrete Probability, Independent Events, Bayes theorem. Random Variables and Distribution functions (Univariate and Multivariate), Expectation and Moments, Independent Random Variables, Marginal and Conditional Distributions. Generating functions and Law of Large Numbers, Characteristic functions. Probability Inequalities (Chebyshev, Markov, Jensen), Modes of Convergence, Weak and Strong Laws of Large Numbers, Central Limit theorems (i.i.d. case).
Unit 3
Estimation: Methods of estimation, Properties of estimators, Confidence Intervals, Cramer- Rao Inequality, Rao-Blackwell theorem, Completeness, Lehmann-Scheffe theorem, Bhattacharya and Chapman -Robins Inequalities.
Unit 4
Testing of Hypotheses: Most Powerful and Uniformly Most Powerful tests, Likelihood Ratio Test, Locally Most Powerful test, Analysis of discrete data, Chi-Square test for goodness of fit, Small and Large sample tests, Invariance tests.
Non-parametric inference: Simple Non-Parametric tests for one and two sample problems, Rank Correlation and test for Independence.
Unit 5
Correlation: Partial and Multiple Correlation Coefficients and related tests.
Regression: Gauss Markov Models, Estimability of Parameters, Best Linear Unbiased Estimators, Simple and
Multiple Linear Regressions, Elementary Regression Diagnostics, General Linear Model, Logistic Regression.
Unit 6
Multivariate Analysis: Multivariate normal distribution, Wishart distribution and its properties, Hotelling’s T2 distribution, Mahalanobis D2 statistic, Distribution of quadratic forms.
Data Reduction Techniques: Principal Component Analysis, Discriminant Analysis, Cluster Analysis, Canonical Correlation, Factor Analysis–EFA and CFA.
Unit 7
Design of Experiments: Analysis of Variance and Covariance, Fixed, Random and Mixed effects models, Randomized Block Designs, Latin-Square Designs, Mutually Orthogonal Latin-Squares and Youden Square Design.
Connectedness and Orthogonality of Block Designs, Balanced Incomplete Block Design–Construction and Analysis.
Partially Balanced Incomplete Block Design, 2k and 3k factorial experiments, Complete & Partial Confounding and construction, Fractional Factorial design–2n-k .
Sampling Techniques–Simple random sampling, Stratified sampling and Systematic sampling, Probability Proportional to Size sampling, Cluster sampling, Multistage sampling, Ratio and Regression estimators, Horvitz–Thompson estimator.
Unit 8
Statistical Quality Control: Quality and Quality Improvement, Statistical Process Control, Control Charts for Attributes and Variables, Schewart Control charts, Operating-Characteristic Function, Process Capability analysis, Process capability ratios, Acceptance Sampling Plans, Dodge–Romig Sampling Plans – AOQL, ATI and LTPD –Continuous Sampling Plans by Attributes, CSP–1, CSP–2 and CSP–3, CUSUM Control Charts.
Reliability: Basics of Reliability–Quality and Reliability–Reliability Modelling. Concepts of Series and Parallel Systems.
Unit 9
Survival Analysis: Survival and Hazard functions, Types of Censoring. Kaplan-Meier Estimator, Cox PH model, Parametric Models.
Bayesian Inference: Bayes theorem, Conjugate, Improper and Jeffreys’ Prior, Loss and Risk functions, Posterior Predictive Distribution, Bayesian Point and Interval Estimates.
Unit 10
Operations Research: Linear Programming Problems, Simplex and Dual Simplex methods, Sensitivity analysis, Integer Programing, Non-Linear Programming, Kuhn-Tucker Condition, Decision Tree and Bellman Principle of Optimality.
Queuing Theory: Elementary Queuing and Inventory Models, Steady-State solutions of Markovian Queuing Models, M/M/1 Model, M/M/1 with limited waiting space, Markov Chains with finite and countable state space, Classification of states, Limiting behaviour of n-step transition probabilities, Stationary distribution, Poisson and Birth-and-Death Processes.
TN TRB Assistant Professor Statistics Exam Pattern 2026
Exam Date 2026 : Notified Soon
Starting Date of Application Form : Notified Soon
Last Date of Application Form : Notified Soon
TN TRB Assistant Professor Syllabus 2026 - Overview
| Conducting Body | Teacher Recruitment Board |
| Name of the Exam | TN TRB Assistant Professor |
| Post Name | Assistant Professor |
| Total Post | Notified Soon |
| Mode of Application | Online |
| College | Government Arts and Science Colleges & Colleges of Education |
| Exam date 2026 | Notified Soon |
| Category | Syllabus and Exam Pattern |
| Job Location | Tamilnadu |
| Official website | https://www.trb.tn.gov.in |
TN TRB Assistant Professor Statistics Syllabus 2026
Paper-I Syllabus :-
Part A: Compulsory Tamil
1. Reading Comprehension
2. Fillers
3. Cloze test
4. Tenses
5. Adjectives
6. Adverbs
7. Prepositions
8. Sentence Completion
9. Paragraph Completion
10. Antonym and synonym
11. Grammatical Error based question
Part B: Concerned Subject - Statistics :
Unit 1
Real Analysis: Set theory, Bolzano Weierstrass theorem, Sequences and Series, Convergence, Sequences and Series of functions, Uniform Continuity, Differentiability, Riemann sums and Riemann Integral.
Linear Algebra: Vector Spaces, Subspaces, Linear Dependence, Basis, Dimension, Algebra of Linear Transformations, Algebra of Matrices, Rank and Determinant of Matrices, Linear Equations, Eigenvalues, Eigenvectors, Cayley-Hamilton theorem. Change of basis, Canonical forms, Diagonal forms, Triangular forms, Jordan forms. Inner Product Spaces, Orthonormal basis. Quadratic forms, Reduction and Classification of Quadratic forms.
Measure Theory: Measurable spaces, Extension of measure, Signed measure, Jordan-Hahn decomposition theorems. Lebesgue measure, Metric Spaces, Convergence, Continuity, Compactness, Connectedness, Monotone Convergence theorem, Fatou’s Lemma, Dominated Convergence theorem, Absolute Continuity of two measures, Radon-Nykodym theorem, Product measures, Fubini’s theorem.
Unit 2
Probability Theory: Sample Space, Discrete Probability, Independent Events, Bayes theorem. Random Variables and Distribution functions (Univariate and Multivariate), Expectation and Moments, Independent Random Variables, Marginal and Conditional Distributions. Generating functions and Law of Large Numbers, Characteristic functions. Probability Inequalities (Chebyshev, Markov, Jensen), Modes of Convergence, Weak and Strong Laws of Large Numbers, Central Limit theorems (i.i.d. case).
Unit 3
Estimation: Methods of estimation, Properties of estimators, Confidence Intervals, Cramer- Rao Inequality, Rao-Blackwell theorem, Completeness, Lehmann-Scheffe theorem, Bhattacharya and Chapman -Robins Inequalities.
Unit 4
Testing of Hypotheses: Most Powerful and Uniformly Most Powerful tests, Likelihood Ratio Test, Locally Most Powerful test, Analysis of discrete data, Chi-Square test for goodness of fit, Small and Large sample tests, Invariance tests.
Non-parametric inference: Simple Non-Parametric tests for one and two sample problems, Rank Correlation and test for Independence.
Unit 5
Correlation: Partial and Multiple Correlation Coefficients and related tests.
Regression: Gauss Markov Models, Estimability of Parameters, Best Linear Unbiased Estimators, Simple and
Multiple Linear Regressions, Elementary Regression Diagnostics, General Linear Model, Logistic Regression.
Unit 6
Multivariate Analysis: Multivariate normal distribution, Wishart distribution and its properties, Hotelling’s T2 distribution, Mahalanobis D2 statistic, Distribution of quadratic forms.
Data Reduction Techniques: Principal Component Analysis, Discriminant Analysis, Cluster Analysis, Canonical Correlation, Factor Analysis–EFA and CFA.
Unit 7
Design of Experiments: Analysis of Variance and Covariance, Fixed, Random and Mixed effects models, Randomized Block Designs, Latin-Square Designs, Mutually Orthogonal Latin-Squares and Youden Square Design.
Connectedness and Orthogonality of Block Designs, Balanced Incomplete Block Design–Construction and Analysis.
Partially Balanced Incomplete Block Design, 2k and 3k factorial experiments, Complete & Partial Confounding and construction, Fractional Factorial design–2n-k .
Sampling Techniques–Simple random sampling, Stratified sampling and Systematic sampling, Probability Proportional to Size sampling, Cluster sampling, Multistage sampling, Ratio and Regression estimators, Horvitz–Thompson estimator.
Unit 8
Statistical Quality Control: Quality and Quality Improvement, Statistical Process Control, Control Charts for Attributes and Variables, Schewart Control charts, Operating-Characteristic Function, Process Capability analysis, Process capability ratios, Acceptance Sampling Plans, Dodge–Romig Sampling Plans – AOQL, ATI and LTPD –Continuous Sampling Plans by Attributes, CSP–1, CSP–2 and CSP–3, CUSUM Control Charts.
Reliability: Basics of Reliability–Quality and Reliability–Reliability Modelling. Concepts of Series and Parallel Systems.
Unit 9
Survival Analysis: Survival and Hazard functions, Types of Censoring. Kaplan-Meier Estimator, Cox PH model, Parametric Models.
Bayesian Inference: Bayes theorem, Conjugate, Improper and Jeffreys’ Prior, Loss and Risk functions, Posterior Predictive Distribution, Bayesian Point and Interval Estimates.
Unit 10
Operations Research: Linear Programming Problems, Simplex and Dual Simplex methods, Sensitivity analysis, Integer Programing, Non-Linear Programming, Kuhn-Tucker Condition, Decision Tree and Bellman Principle of Optimality.
Queuing Theory: Elementary Queuing and Inventory Models, Steady-State solutions of Markovian Queuing Models, M/M/1 Model, M/M/1 with limited waiting space, Markov Chains with finite and countable state space, Classification of states, Limiting behaviour of n-step transition probabilities, Stationary distribution, Poisson and Birth-and-Death Processes.
TN TRB Assistant Professor Statistics Exam Pattern 2026
| Paper | Section | Subject | No.of Question | Each Question carries | Marks | Duraion |
| Paper 1 | Part A (MCQ) | Compulsory Tamil | 30 | (20 x 2=40 marks 10 x 1=10 marks) |
50 | 3 Hour |
| Part B (MCQ) | Concerned Subject | 100 | 1.5 marks |
150 | ||
| Paper 2 | Descriptive type (on general topics) | One essay type question out of 5 questions (Maximum 300 words) |
- | 50 | 1 Hour |
Exam Date 2026 : Notified Soon
Starting Date of Application Form : Notified Soon
Last Date of Application Form : Notified Soon
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TN TRB Assistant Professor Statistics Exam Paper 1 - English130 questions • 180 mins • 200 marks
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TN TRB Assistant Professor Statistics Exam Paper 1 - English130 questions • 180 mins • 130 marks
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