Statistics Optional Syllabus for UPSC
The UPSC Statistics optional is examined in two Mains papers of 250 marks each, 500 marks in total. Paper I has 4 topics and Paper II has 4 topics, listed below with their subtopics.
Statistics Paper I syllabus
1. Probability Theory
- Sample space, events, probability measure, random variable as measurable function
- Distribution functions — discrete & continuous; probability mass & density functions
- Expectation, moments, conditional expectation; convergence of random variables
- Probability generating function, MGF, characteristic function; CLT (Lindeberg-Levy form)
2. Statistical Inference
- Consistency, unbiasedness, efficiency, sufficiency, completeness — properties of estimators
- UMVU estimation — Rao-Blackwell, Lehmann-Scheffe theorems; Cramer-Rao inequality
- Methods of estimation — MOM, MLE, least squares, minimum chi-square; Bayes estimators
- Non-parametric tests — Kolmogorov-Smirnov, Wilcoxon, Mann-Whitney, sign test; SPRT (Wald)
3. Linear Inference & Multivariate Analysis
- Linear statistical models, theory of least squares, Gauss-Markoff theory
- Analysis of variance — one-way, two-way, three-way; regression — linear, curvilinear, multiple
- Multiple & partial correlations; estimation of variance & covariance components
- Multivariate normal distribution; Mahalanobis D², Hotelling T²; discriminant, canonical, PCA
4. Sampling Theory & Design of Experiments
- SRS with/without replacement; stratified, systematic, cluster, multistage sampling
- Ratio & regression estimation; two-phase sampling; PPS sampling
- CRD, RBD, LSD & their analyses; BIBD; missing plot technique
- Factorial experiments — 2^n, 3^2; confounding; split-plot design; Duncan's multiple range test
Statistics Paper II syllabus
1. Industrial Statistics
- Process & product control; control charts — X-bar, R, s, p, np, c charts; CUSUM chart
- Acceptance sampling — single, double, multiple, sequential plans; OC, ASN, AOQ curves
- Concepts of AQL, LTPD, AOQL; Dodge-Romig tables
- Reliability — failure rate, reliability functions; series & parallel systems; exponential & Weibull models
2. Optimization Techniques
- Operations Research models; simulation & Monte-Carlo methods
- Linear programming — simplex, two-phase method, M-technique; duality; sensitivity analysis
- Transportation & assignment problems; rectangular games; two-person zero-sum games
- Replacement policies; inventory models — deterministic & stochastic; queuing — M/M/1, M/M/K
3. Quantitative Economics & Official Statistics
- Time series — trend, seasonal, cyclical; Box-Jenkins ARIMA; stationarity tests
- Index numbers — Laspeyre's, Paasche's, Fisher's; uses, limitations; tests for index numbers
- General linear model — OLS, GLS; multicollinearity, autocorrelation, heteroscedasticity
- National accounts; price statistics; agricultural & industrial production indices; official statistical systems
4. Demography & Vital Statistics
- Sources of demographic data — census, vital registration, surveys
- Measures of fertility — CBR, GFR, TFR; mortality — CDR, IMR, life tables
- Population growth models — Malthusian, logistic; stable & stationary populations
- Population projections — component method; urbanisation; migration analysis
Other Sciences optionals
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Follow Paper I and Paper II topic by topic, with revision counts — free.
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