Video Lectures of Statistics Optional for UPSC for UPSC CSE Exam
Watch free video lectures for Statistics Optional for UPSC covering all chapters/topics as per the latest syllabus in 2026. These concept videos, recorded lectures, and audio notes are designed to help UPSC CSE students understand every topic clearly — anytime, anywhere. Start learning on EduRev.
Probability
| Sample Space & Events 05:43 min |  |
| Overview Of Random Variable & Probability Distribution 08:00 min | |
| Random Variable, Probability Mass Function, Distribution Function 18:38 min | |
| Random Variable, Probability Density Function, Cumulative Distribution Function 21:22 min | |
| Joint Probability Distribution , Joint PMF, Marginal PMF, Bivariate RV 20:45 min | |
| Joint Probability Distribution , Joint PMF, Marginal PMF, Statistical Independence 16:15 min | |
| Mathematical Expectation, Variance Of Continuous & Discrete Random Variable 12:48 min | |
| Skewness & Kurtosis, Moments, Leptokurtic, Mesokurtic and Platykurtic 17:37 min | |
| Skewness & Kurtosis, Moments, Leptokurtic, Mesokurtic and Platykurtic Examples 19:32 min | |
| Marginal & Conditional Distributions 12:24 min | |
| Independence of Random Variables 05:08 min | |
| Mathematical Expectation, Variance Of Continuous & Discrete Random Variable 12:48 min | |
| Conditional Expectation 04:31 min | |
| Convergence in Probability 05:08 min | |
| Convergence of a Sequence of Random Variable in Distribution 08:28 min | |
| Chebyshev’s Inequality 05:57 min | |
| Khintchine’s weak law of Large Numbers 07:31 min | |
| Strong Law of Large Numbers 24:52 min | |
| Kolmogoroffs Theorems 11:27 min | |
| Probability Generating Function 20:02 min | |
| Moment Generating Function 25:45 min | |
| Characteristic Function 18:59 min | |
| Inversion Theorem 08:41 min | |
| Lindenberg & Levy forms of Central Limit Theorem 15:43 min | |
| Standard Discrete & Continuous Probability Distributions 43:06 min | |
Statistical Inference
| Unbiasedness & Consistency 16:03 min | |
| Statistical Inference: Completeness 12:40 min | |
| Ancillary Statistic 06:18 min | |
| Factorization Theorem 33:31 min | |
| Exponential Family of Distribution & its Properties 09:18 min | |
| Uniformly Minimum Variance Unbiased (UMVU) Estimation 16:40 min | |
| Rao Blackwell Theorem 07:38 min | |
| Lehmann-Scheffe Theorem 07:01 min | |
| Cramer-Rao Inequality & Its Proof 08:36 min | |
| Estimation by methods of moments 22:21 min | |
| Methods of Maximum Likelihood & its Properties 08:45 min | |
| Least Squares Method 15:05 min | |
| Chi-Square Test 05:23 min | |
| Asymptotic Efficiency 14:25 min | |
| Prior & Posterior Distributions 11:51 min | |
| Loss function, Risk function, & Bayes Estimator 14:15 min | |
| Randomised Tests 08:57 min | |
| MP tests & Neyman-Pearson lemma 26:54 min | |
| Monotone Likelihood Ratio: Similar & Unbiased Tests 33:51 min | |
| Likelihood Ratio Test & Its Asymptotic Distribution 07:04 min | |
| Confidence Intervals & its Relation with Tests 29:02 min | |
| Kolmogorov’s Test for Goodness of Fit & its Consistency 25:44 min | |
| Sign Test & its optimality 26:04 min | |
| Wilcoxon Signedranks Test & its consistency 18:13 min | |
| Kolmogorov-Smirnov Two Sample Test 13:45 min | |
| Wilcoxon-MannWhitney test 14:26 min | |
| Wald’s SPRT & Its properties 09:39 min | |
| Bernoulli Distributions 09:18 min | |
| Binomial Distributions 11:32 min | |
| Wald’s Fundamental Identity 19:14 min | |
Linear Inference and Multivariate Analysis
| Linear Statistical Models 11:24 min | |
| Analysis of Variance 13:29 min | |
| Gauss-Markoff Theorem 23:08 min | |
| Least Squares Estimates & Their precision 13:38 min | |
| Tests of Significance 30:25 min | |
| Interval Estimates 08:24 min | |
| Regression Analysis: Models, Lines & Coefficients 24:37 min | |
| Regression Analysis:Simple, Multiple Linear, Curvilinear & Logistic Regression 15:37 min | |
| Orthogonal Polynomials 17:04 min | |
| Estimation of Variance & Covariance Components 26:05 min | |
| Multivariate Normal Distribution 35:24 min | |
| Hotelling’s T2 Statistics: Their applications & properties 06:50 min | |
| Discriminant Analysis 08:33 min | |
| Canonical Correlations 06:26 min | |
| Principal Component Analysis 28:06 min | |
Sampling Theory and Design of Experiments
| Distinctive Features of Finite Population Sampling 31:40 min | |
| Probability Sampling Design 09:49 min | |
| Simple Random Sampling with & without replacement 07:01 min | |
| Stratified Random Sampling 10:48 min | |
| Systematic Sampling & its Efficacy 06:08 min | |
| Cluster Sampling 10:55 min | |
| Two Stage Sampling 16:26 min | |
| Ratio & Regression Methods of Estimation 49:10 min | |
| Two-phase Sampling 13:28 min | |
| Horvitz Thompson Estimators 05:54 min | |
| The Hansen-Hurwitz Estimators 09:45 min | |
| Statistical Errors: Sampling and Non-Sampling Error 09:50 min | |
| Fixed effects model vs Random effects model 05:09 min | |
| CRD, RBD, LSD & their Analyses 08:19 min | |
| Incomplete Block Designs 15:46 min | |
| Blocking & Confounding System for Two Level Factorial 11:25 min | |
| Duncan’s Multiple Range Test 03:59 min | |
Industrial Statistics
| Process & Product Control: Statistics Quality Control 05:24 min | |
| Control Charts: Purpose, Advantages & Types 12:21 min | |
| Control Charts for Variables & Attributes 15:05 min | |
| Cumulative Sum Chart 29:23 min | |
| Single Sampling Plan 02:37 min | |
| Double Sampling Plan 03:46 min | |
| Multiple Sampling Plan 14:21 min | |
| Sequential Sampling Plan 07:47 min | |
| OC, ASN, AOQ and ATI curves 22:51 min | |
| Producer's Risk & Consumer’s Risk 09:42 min | |
| AQL, LTPD and AOQL 14:20 min | |
| Acceptance Sampling Plans for Variables 42:44 min | |
| Dodge-Romig Sampling Plan 09:08 min | |
| Concept of Reliability & System Failure 12:48 min | |
| System Reliabilty: Components in Series & Parallel 08:57 min | |
| Renewal Function & Renewal Equation 46:48 min | |
| Failure models: Weibull and Lognormal Distributions 07:13 min | |
Optimization Techniques
| Models in Operations Research 12:36 min | |
| Formulation of Linear Programming (LP) problem 15:34 min | |
| Simple LP model & its Graphical Solution 17:19 min | |
| The Simplex Procedure 26:31 min | |
| The Two-phase Simplex Method 30:20 min | |
| The M-technique with Artificial Variables 31:50 min | |
| The Duality Theory of LP & its Economic Interpretation 30:25 min | |
| Sensitivity Analysis in Linear Programming 09:22 min | |
| Introduction to North West Corner Method; Transportation problem & LPP 29:47 min | |
| Rectangular Game with Simplex method of LPP 25:58 min | |
| Game Theory: Two-person Zero Sum Games 15:37 min | |
| Replacement Problem: Replacement Situation & Individual Replacement 10:21 min | |
| Inventory management and analytical structure of inventory problems 32:34 min | |
| Deterministic Model vs Stochastic Model 01:52 min | |
| Discrete Time- Markov Chains 29:40 min | |
| Transition Probability Matrix 29:30 min | |
| Classisification of States & Markov Chains 25:01 min | |
| Continuous-time Markov chains 42:26 min | |
| Concept of Poisson process 28:12 min | |
| Elements of Queuing Theory 17:59 min | |
Quantitative Economics and Official Statistics
| Components of Time Series 11:41 min | |
| Box-Jenkins Method 17:59 min | |
| Tests for Stationary Series 08:16 min | |
| ARIMA models in Time Series 10:17 min | |
| Index Numbers: Meaning, Types & Uses 09:07 min | |
| Introduction to Time reversal test; Factor reversal test; Circular test 37:22 min | |
| Laspeyre’s, Paasche’s & Fisher’s ideal index numbers 06:18 min | |
| Chain Base Index Numbers 05:17 min | |
| Index of Industrial Production 27:03 min | |
| Consumer Price Index 40:47 min | |
| Agricultural Production Index 02:18 min | |
| Wholesale Price Index 14:16 min | |
| Limitations of Index Numbers 09:24 min | |
| General Linear Model 43:43 min | |
| Ordinary Least Square Method 02:10 min | |
| Generalized Least Squares Method of Estimation 13:13 min | |
| Problem of Multi-collinearity 10:46 min | |
| Consequences & Solutions of Multi-collinearity 06:58 min | |
| Autocorrelation & its Consequences 13:40 min | |
| Heteroscedasticity of Disturbances & its Testing 15:37 min | |
| Simultaneous Equation Models: Concept 20:49 min | |
| Identification Problem: Simultaneous Equation Models 12:13 min | |
| Rules for Identification: Order & Rank Conditions 12:27 min | |
| Two Stage Least Squares Method 05:04 min | |
| Present Official Statistical System in India 19:32 min | |
| Official Statistics: Theory & Methods 05:43 min | |
Demography and Psychometry
| Data Sources for Demographic Studies & Agencies involved 08:14 min | |
| Vital Statistics 05:45 min | |
| Vital Statistics - Demography - Part 2 - CDR Solved Example - Statistics 04:30 min | |
| Vital Statistics - Demography - Part 3 - CDR Solved Example - Statistics 05:46 min | |
| Vital Statistics - Demography - Part 4 - Age Specific Death Rate - Statistics 04:47 min | |
| Vital Statistics - Demography - Part 5 - Standardized Death Rate - Statistics 05:28 min | |
| Vital Statistics - Demography - Part 6 - STDR Example - Statistics 06:41 min | |
| Vital Statistics - Demography - Part 7 - Life Table - Mortality Table - Statistics 11:07 min | |
| Vital Statistics - Demography - Part 8 - Life Table Solved Example - Statistics 06:25 min | |
| Vital Statistics - Demography - Part 9 - Life Table Solved Example - Statistics 04:46 min | |
| Vital Statistics - Demography - Part 10 - Life Table Solved Example - Statistics 04:02 min | |
| Vital Statistics -Demography- Part 12-Infant Mortality Rate and Neonatal Mortality Rate - Statistics 05:44 min | |
| Logistic Curve Method: Numerical 03:49 min | |
| Estimating Population Parameters 17:51 min | |
| Estimation of Population Parameters Using Moments 42:30 min | |
| Normalization vs Standardization 08:00 min | |
| Standard Scores: Z-scores & T-scores 18:51 min | |
| Intelligence quotient and its measurement and uses 05:27 min | |
| Validity vs Reliability 03:53 min | |
| Methods to test Reliabilty 04:17 min | |
| Factor Analysis [PSY] 31:46 min | |
