The Indian Forest Service (IFS) Statistics optional syllabus for the UPSC exam consists of two papers: Paper I and Paper II. Each paper is designed to test a candidate’s understanding of statistical concepts, methods, and applications. Here’s the detailed syllabus:
Paper I
1. Probability
- Sample space and events.
- Probability axioms.
- Conditional probability and independence.
- Bayes’ theorem.
- Random variables.
- Probability distributions.
- Expectations and moments.
- Moment generating functions.
- Chebyshev’s inequality.
2. Statistical Methods
- Measures of central tendency and dispersion.
- Correlation and regression.
- Multiple and partial correlation.
- Rank correlation.
- Curve fitting by least squares.
- Theory of attributes.
- Consistency of data.
- Independence and association of attributes.
3. Estimation
- Properties of estimators.
- Methods of estimation.
- Maximum likelihood estimation.
- Confidence intervals.
4. Testing of Hypotheses
- Simple and composite hypotheses.
- Neyman-Pearson theory.
- Likelihood ratio tests.
- Tests based on normal, t, chi-square, and F distributions.
5. Sampling Theory and Design of Experiments
- Simple random sampling.
- Stratified sampling.
- Systematic sampling.
- Cluster and multistage sampling.
- Ratio and regression methods of estimation.
- Analysis of variance.
- Principles of experimental design.
- Completely randomized design.
- Randomized block design.
- Latin square design.
- Factorial experiments.
Paper II
1. Stochastic Processes and Queuing Theory
- Markov processes.
- Poisson processes.
- Birth and death processes.
- Queueing systems: M/M/1, M/M/c, M/G/1.
2. Statistical Inference
- Sufficiency.
- Completeness.
- Exponential families.
- Methods of moments.
- Interval estimation.
- Testing of hypotheses.
- Sequential tests.
3. Multivariate Analysis
- Multivariate normal distribution.
- Estimation of mean vector and covariance matrix.
- Principal component analysis.
- Canonical correlations.
- Discriminant analysis.
4. Linear Models and Regression Analysis
- Linear models.
- Least squares estimators.
- Gauss-Markov theorem.
- Multiple regression.
- Testing of linear hypotheses.
- Generalized least squares.
5. Sample Surveys
- Simple random sampling.
- Stratified sampling.
- Systematic sampling.
- Cluster sampling.
- Two-stage and multi-stage sampling.
- Non-sampling errors.
- Preparation of schedules and questionnaires.
6. Operations Research
- Linear programming.
- Simplex method.
- Duality.
- Transportation and assignment problems.
- Game theory.
- Inventory models.
- Replacement problems.
- Dynamic programming.
- Non-linear programming.
7. Econometrics
- Scope and method of econometrics.
- Simple and multiple linear regression models.
- Ordinary least squares estimation.
- Generalized least squares.
- Errors in variables.
- Simultaneous equation models.
- Identification problem.
- Instrumental variable estimation.
- Two-stage least squares estimation.
This syllabus is comprehensive, covering a wide range of statistical concepts and techniques. Candidates opting for this subject should have a strong foundation in statistics and be well-versed in both theoretical and applied aspects.
