UPPSC Statistics Assistant Professor Syllabus, Eligibility – GDC Examination 2025

September 17, 2025

The Uttar Pradesh Public Service Commission (UPPSC) conducts the Assistant Professor Examination for Government Degree Colleges (GDC). Aspirants for the Statistics Assistant Professor post must have a clear understanding of the syllabus and eligibility criteria before starting their preparation. Below is the complete and updated syllabus for the UPPSC Statistics Assistant Professor Exam 2025, along with the essential eligibility details.

UPPSC Statistics Assistant Professor Syllabus 2025

UNIT 1 – Probability Theory

  • Random Experiment, Sample Space, Events, Algebra of Events

  • Definitions of Probability, Probability Space, Boole’s Inequality

  • Conditional Probability, Total & Compound Theorem, Bayes Theorem

  • Independence of Events

  • Discrete & Continuous Random Variables – PMF, PDF, Distribution Function

  • Expectation, Moments, Cumulants, Moment Generating Function, Characteristic Function

  • Chebyshev’s and Markov’s Inequalities

  • Types of Convergences: In Probability, Distribution, r-th Mean, Almost Sure

  • Laws of Large Numbers (WLLN, SLLN), Khinchin’s & Kolmogorov’s Theorems

  • Central Limit Theorem (CLT): Lindeberg-Levy, Liapunov, Lindeberg-Feller

UNIT 2 – Distribution Theory

  • Bivariate Distributions: Joint, Marginal, Conditional

  • Independence of Random Variables

  • Discrete Distributions: Binomial, Poisson, Negative Binomial, Geometric, Uniform, Hypergeometric, Multinomial

  • Continuous Distributions: Normal, Gamma, Beta, Exponential, Laplace, Cauchy, Weibull, Pareto, Log-Normal, Bivariate Normal

  • Sampling Distributions: Chi-Square, t, F Distributions, Their Properties

  • Order Statistics: Smallest, Largest, r-th Order, Joint Distributions, Median, Range

UNIT 3 – Estimation Theory

  • Point Estimation: Unbiasedness, Consistency, Efficiency, Cramer-Rao Bound, BLUE

  • Sufficiency, Completeness, Rao-Blackwell & Lehmann-Scheffe Theorems

  • Estimation Methods: Method of Moments, Maximum Likelihood, Least Squares

  • Bayesian Estimation: Prior, Posterior, Bayes Risk, Loss Function

  • Interval Estimation: Confidence Intervals using Pivots for Large Samples

UNIT 4 – Testing of Hypothesis

  • Fundamentals of Hypothesis Testing, Types of Errors, Critical Regions

  • Neyman–Pearson Lemma, Most Powerful & Uniformly Most Powerful Tests

  • Likelihood Ratio Tests (LRT), Sequential Probability Ratio Tests (SPRT)

  • Tests based on t, F, Chi-square, Fisher’s Z-Transformation

  • Non-parametric Tests: Sign Test, Signed Rank Test, Median Test, Run Test, Mann-Whitney U-Test, Wilcoxon Test, Goodness of Fit (Chi-square, Kolmogorov–Smirnov)

UNIT 5 – Survey Sampling

  • Sampling Design & Schemes – Probability & Non-Probability Sampling

  • Simple Random Sampling (with/without replacement), Horvitz–Thompson, Desraj Method

  • Stratified Sampling: Optimum Allocation, Gain in Precision, Post-Stratification

  • Systematic Sampling, Cluster Sampling, Two-Stage & Two-Phase Sampling

  • Ratio & Regression Estimation, Product Estimator, Non-Sampling Errors

UNIT 6 – Linear Estimation & Design of Experiments

  • Ordinary Least Squares Estimation (OLSE), BLUE, Hypothesis Testing in Regression

  • Quadratic Forms & g-inverse, ANOVA & ANCOVA (One-way & Two-way)

  • Experimental Designs:

    • Completely Randomized Design (CRD)

    • Randomized Block Design (RBD)

    • Latin Square Design (LSD)

    • Balanced Incomplete Block Design (BIBD)

    • Partially Balanced Incomplete Block Design (PBIBD)

    • Split Plot Design

    • Factorial Experiments (2², 3², 3³), Confounding

UNIT 7 – Linear Algebra & Multivariate Analysis

  • Matrix Theory: g-inverse, Orthogonal Matrices, Idempotent Matrices

  • Characteristic Roots & Vectors, Quadratic Forms, Simultaneous Reduction

  • Multivariate Analysis:

    • Multivariate Normal Distribution

    • Wishart Distribution

    • Hotelling’s T² & Mahalanobis D² Statistics

    • Discriminant Analysis, PCA, Canonical Correlations, Factor Analysis

UNIT 8 – Applied Statistics

  • Statistical Quality Control (SQC): Control Charts (X̄, R, s, np, p, c, u)

  • Sampling Inspection Plans: OC, AQL, LTPD, AOQL, ASN, ATI

  • Time Series Analysis: Trend, Seasonal, Cyclical Variations

  • Index Numbers: Laspeyre’s, Paasche’s, Marshall-Edgeworth, Fisher’s Ideal, Time & Factor Reversal Tests

  • Vital Statistics: CDR, SDR, IMR, Life Tables, Fertility Rates, Population Growth Rates

  • Indian Official Statistics & Important Data Related to Uttar Pradesh

General Studies (Common for All Subjects)

Apart from the subject syllabus, candidates must prepare for General Studies, which is common for every subject in the UPPSC GDC Assistant Professor Examination.

  • General Science

  • Current Events of National and International Importance

  • History of India (Including Indian National Movement)

  • Indian Polity & Economy

  • Geography – Indian & World

  • Mental Ability & Statistical Analysis
    (Special reference to Uttar Pradesh is expected)

UPPSC Statistics Assistant Professor Eligibility 2025

Option A: Master’s Degree + NET/SET/SLET

A Master’s degree with 55% marks (or equivalent grade) in Statistics or a relevant/allied subject from an Indian University,
OR an equivalent degree from an accredited foreign university.

Additionally, candidates must have cleared the National Eligibility Test (NET) conducted by UGC/CSIR or an equivalent accredited test like SLET/SET.

Candidates with a Ph.D. Degree as per UGC Regulations (2009/2016 & amendments) are exempt from NET/SLET/SET, provided they fulfill the following conditions (for Ph.D. registered before July 11, 2009):

  • Ph.D. awarded in regular mode.

  • Thesis evaluated by at least two external examiners.

  • Open Ph.D. viva voce conducted.

  • At least two research papers published from Ph.D. work (one in a refereed journal).

  • At least two papers presented in UGC/ICSSR/CSIR-sponsored seminars/conferences.

Certification must be provided by the Registrar/Dean (Academic Affairs) of the awarding University.

Note: NET/SLET/SET exemption applies to subjects where these tests are not conducted.

Option B: Ph.D. from Top 500 Foreign Universities

A Ph.D. degree from a foreign university/institution ranked among the top 500 in global rankings by:

    • QS (Quacquarelli Symonds)

    • Times Higher Education (THE)

    • Academic Ranking of World Universities (ARWU) by Shanghai Jiao Tong University

Conclusion

The UPPSC Statistics Assistant Professor syllabus covers probability, distribution theory, estimation, hypothesis testing, sampling, multivariate analysis, and applied statistics. Focused study, practice, and revision will help aspirants excel and secure a government teaching position in 2025.

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