MCQs GIVEN AS PDF ONLY

UGC NET Statistics (Code 107): B-Series Practice MCQs · Unit 1: Probability and Distributions · Unit 2: Real Analysis and Matrix Algebra · Unit 3: Sampling Methods and Design of Experiments · Unit 4: Estimation Theory · Unit 5: Testing of Hypotheses · Unit 6: Linear Estimation, Regression Analysis and Econometrics · Unit 7: Time Series · Unit 8: Multivariate Analysis · Unit 9: Stochastic Processes · Unit 10: Indian Statistical System and R Software

Statistics A01 Probability and Distributions

How to Use This Unit: Exam Approach · Overview and Foundations of Probability · Conditional Probability & Bayes’ Theorem · Random Variables and Distribution Functions · Expectation, Moments & Moment Generating Function · Standard Discrete Distributions · Standard Continuous Distributions · Exam Mastery Block · Joint Distributions, Marginal & Conditional · Chebyshev Inequality & Other Inequalities · Sampling Distributions · Transformation of Random Variables · Characteristic Function & its Properties · Modes of Convergence & Laws of Large Numbers · Central Limit Theorems · Exam Mastery Block (Objective) · Exam Practice Zone: Unit I

Statistics A02 Real Analysis and Matrix Algebra

How to Use This Unit: Exam Approach · Sets: Finite, Countable, and Uncountable · Series of Real Numbers and Power Series · Limit, Continuity and Uniform Continuity · Differentiability and Mean Value Theorems · Riemann Integration and Improper Integrals · Functions of Two Variables: Limits, Partial Derivatives, Total Derivative · Maxima, Minima, Saddle Points, and Lagrange Multipliers · Objective Exam Focus · Double and Triple Integrals and Applications · Vector Spaces, Subspaces, Basis, Dimension · Row Space, Column Space, Rank, Nullity, and Row Reduced Echelon Form · Determinant, Trace, and Inverse of a Matrix · Gram-Schmidt Orthogonalization and Orthogonal Projections · Eigenvalues, Eigenvectors, Cayley-Hamilton Theorem · Symmetric, Skew-Symmetric, Orthogonal Matrices; Positive Definiteness; Quadratic Forms · Key Facts to Memorise · Common Confusions & Examiner Traps · One-Look Revision · Exam Practice Zone: Unit II

Statistics A03 Sampling Methods and Design of Experiments

How to Use This Unit: Exam Approach · Overview of Sampling Methods · Simple Random Sampling (SRS) · Stratified Random Sampling · Systematic Sampling · Ratio and Regression Estimation · Cluster Sampling · Sampling with Varying Probabilities and Double Sampling · Principles of Design of Experiments and ANOVA · Completely Randomized, Randomized Block, and Latin Square Designs · Factorial Experiments and Confounding · Incomplete Block Designs and BIBD · Intra-block and Inter-block Analysis of BIBD · Examination Booster for Sampling · Objective Exam Focus · Examination Booster for Design of Experiments · Quick Revision Summary · Gap Chapter: PPS Without Replacement, Ordered and Unordered Estimators, and Non-negative Variance Estimation · Exam Practice Zone: Unit III

Statistics A04 Estimation Theory

How to Use This Unit: Exam Approach · Overview, Definitions & Etymology · Historical Evolution & Major Thinkers · Exam Mastery Block · Properties of Point Estimators · Method of Moments (MOM) · Maximum Likelihood Estimation (MLE) · Sufficiency, Factorization Theorem & Minimal Sufficiency · UMVUE, Rao-Blackwell & Lehmann-Scheffé Theorems · Interval Estimation and the Pivotal Method · Objective Exam Focus · Nonparametric Inference: Order Statistics & EDF · Nonparametric Inference: Rank Correlation · Comparative Analysis: MLE vs. MOM vs. Bayes · Criticism & Debates in Estimation Theory · Contemporary Relevance & Applications · Exam Booster: Problem Types & Tactics · Quick Revision: Key Theorems & Formulae · Gap Chapter: Model Cards for Point Estimation · Exam Practice Zone: Unit IV · Estimation Theory: 50 Examination-Critical Objective Facts

Statistics A05 Testing of Hypotheses

How to Use This Unit: Exam Approach · Basic Concepts of Hypothesis Testing · Neyman-Pearson Lemma and Optimal Tests · Families with Monotone Likelihood Ratio and UMP Tests · Uniformly Most Powerful Unbiased and Invariant Tests · Likelihood Ratio Tests · Wald's Sequential Probability Ratio Test (SPRT) · Chi-square Goodness-of-Fit Test · Chi-square Tests of Independence and Homogeneity · Sign Test and Wilcoxon Signed Rank Test · Mann-Whitney U Test (Wilcoxon Rank Sum Test) · Linear Rank Tests for Location and Scale · Kruskal-Wallis Test · Applications to One-Sample and Two-Sample Problems · Testing of Hypotheses: Examination Booster and Quick Revision · Gap Chapter: Which Test, When? · Exam Practice Zone: Unit V

Statistics A06 Linear Estimation Regression Analysis and Econometrics

How to Use This Unit: Exam Approach · Introduction to Linear Regression and Gauss-Markov Setup · Ordinary Least Squares (OLS) Estimation · Maximum Likelihood Estimation in Linear Regression · ANOVA and Coefficient of Determination (R², Adjusted R²) · Tests of Hypotheses and Linear Restrictions · Generalized Least Squares and Weighted Least Squares · Dummy Variables and Qualitative Regressors · Multicollinearity: Detection and Remedies · Heteroscedasticity: Detection and Remedies · Autocorrelation: Detection and Remedies (Durbin-Watson) · Logistic Regression Models · Restricted Regression under Exact, Stochastic, and Mixed Restrictions · Models with Stochastic Regressors and Errors-in-Variables · Instrumental Variable Estimation and the k‑Class of Estimators · Simultaneous Equations Models: Identification and Estimation (2SLS) · Gap Chapter: Correlation Algebra and Assumption Violations · Exam Practice Zone: Unit VI

Statistics A07 Time Series

How to Use This Unit: Exam Approach · Time Series: Overview and Foundational Concepts · Historical Evolution & Thinkers in Time Series Analysis · Descriptive Measures & Exploratory Analysis · Autocovariance, ACF, PACF & Correlogram · Stationarity & Ergodicity · Strict Stationarity (Strong) vs. Weak (Covariance) Stationarity · Ergodicity: Time Averages vs. Ensemble Averages · Ergodicity Theorem (Formal) · Gaussian Stationary Processes: Strict = Weak · Checking Stationarity: ACF Decay and Unit Root Tests · Ergodicity Conditions: What to Know · Special Case: Cyclical/Periodic Non-stationarity · Wrapping Up: Application in Practice · Wold Decomposition & General Linear Process · Moving Average (MA) Processes · Exam Mastery Block · Autoregressive (AR) Processes · Mixed ARMA Processes & Yule-Walker Equations · Model Identification, Estimation & Order Selection · Forecasting with Stationary & Invertible Processes · Non-Stationarity & ARIMA Models (including Random Walk) · Frequency Domain Analysis & Spectral Density · Examination Booster & Quick Revision · ARCH and GARCH Models: Volatility Modeling in Time Series · Gap Chapter: Model Cards for Time Series · Exam Practice Zone: Unit VII

Statistics A08 Multivariate Analysis

How to Use This Unit: Exam Approach · Matrix Toolkit for Multivariate Analysis · Multivariate Data and Its Summary Measures · The Multivariate Normal Distribution · Estimation of the Mean Vector and Covariance Matrix · The Wishart Distribution · Simple, Partial and Multiple Correlation · Hotelling's T² and Inference on Mean Vectors · MANOVA and Tests on Covariance Matrices · Discriminant Analysis and Classification · Principal Component Analysis · Canonical Correlation Analysis · Factor Analysis · Key Derivations, Step by Step · Complete Case Study: One Data Set, Every Technique · Who Did What: Originators and Indian Contributions · Supporting Topics: Multivariate Regression and Profile Analysis · Trap Compendium: Fifty Statements Examiners Like · Exam Practice Zone for Unit VIII

Statistics A09 Stochastic Processes

How to Use This Unit: Exam Approach · Introduction to Stochastic Processes: Fundamental Concepts and Definitions · Historical Development and Pioneering Contributors · Markov Chains: State Classification, Transience, and Recurrence · Chapman–Kolmogorov Equations and n‑Step Transition Probabilities · Limiting Behavior and Stationary Distributions in Markov Chains · Gambler’s Ruin and Simple Random Walks · The Poisson Process: Properties and Associated Distributions · Birth–Death Processes: Theory and Applications · The M/M/1 Queueing System: Analysis and Performance Measures · Comparative Analysis of Stochastic Process Types · Formula Compendium for Stochastic Processes · Examination Strategies: Common Problem Types and Pitfalls · Quick Revision and Applied Case Studies · Exam Practice Zone for Unit IX

Statistics A10 Indian Statistical System and R Software

How to Use This Unit: Exam Approach · The Indian Statistical System · Census and Large-Scale Sample Surveys · Indian Statisticians and Their Contributions · R Software I: The Language, Calculator and Vectors · R Software II: Matrices, Control Flow and Functions · R Software III: Strings, Lists, Factors and Data Frames · Word Processing and Documentation Software · Exam Practice Zone for Unit X