UPSC IFS 2020 Statistics syllabus,UPSC Indian Forest Services ( IFS ) Exam Statistics syllabus

Statistics syllabus - UPSC IFS UPSC Exam

UPSC IFS Statistics Syllabus

Paper - I


  1. Sample space and events
  2. probability measure and probability space
  3. random variable as a measurable function
  4. distribution function of a random variable
  5. discrete and continuous-type random variable
  6. probability mass function, probability density function
  7. vector-valued random variable
  8. marginal and conditional distributions
  9. stochastic independence of events and of random variables
  10. expectation and moments of a random  variable
  11. conditional expectation
  12. convergence of a sequence of random variable in distribution in probability
  13. pth mean and almost every where
  14. criteria and inter-relations
  15. Borel-Cantelli lemma
  16. Chebyshev’s and Khinchine’s weak laws of large numbers
  17. strong law of large numbers and Kolmogorov’s theorems
  18. Glivenko-Cantelli theorem
  19. probability generating function
  20. characteristic function
  21. inversion theorem
  22. Laplace transform
  23. related uniqueness and continuity theorems
  24. determination of distribution by its moments
  25. Linderberg and Levy forms of central limit theorem
  26. standard discrete and continuous probability distributions
  27. their interrelations and limiting cases
  28. simple properties of finite Markov chains

Statistical Inference: 

  1. Consistency
  2. Unbiasedness
  3. Efficiency
  4. Sufficiency
  5. minimal sufficiency
  6. completeness
  7. ancillary statistic
  8. factorization theorem
  9. exponential family of distribution and its properties
  10. uniformly minimum variance unbiased (UMVU) estimation
  11. Rao-Blackwell and Lehmann- Scheffe theorems
  12. Cramer-Rao inequality for single and several-parameter family of distributions
  13. minimum variance bound estimator and its properties
  14. modifications and extensions of Cramer-Rao inequality
  15. Chapman-Robbins inequality, Bhattacharya’s bounds
  16. estimation by methods of moments, maximum likelihood
  17. least squares
  18. minimum chisquare
  19. modified minimum chi-square properties of maximum likelihood
  20. other estimators,
  21. idea of asymptotic efficiency
  22. idea of prior and posterior distributions
  23. Bayes
  24. estimators
  25. Non-randomised and randomised tests
  26. critical function
  27. MP tests
  28. Neyman- Pearson lemma
  29. UMP tests, monotone likelihood ratio
  30. generalised Neyman- Pearson lemma
  31. similar and unbiased tests
  32. UMPU tests for single and severalparameter families of distributions
  33. likelihood rotates and its large sample properties
  34. chi-square goodness of fit test and its asymptotic distribution.
  35. Confidence bounds and its relation with tests
  36. uniformly most accurate (UMA) and UMA unbiased confidence bounds.
  37. Kolmogorov’s test for goodness of fit and its consistency
  38. sign test and its optimality
  39. Wilcoxon signed-ranks test and its consistency
  40. Kolmogorov-Smirnov twosample test
  41. run test
  42. Wilcoxon-Mann- Whitney test and median test
  43. their consistency and asymptotic normality
  44. Wald’s SPRT and its properties
  45. OC and ASN functions
  46. Wald’s fundamental identity
  47. sequential estimation

Linear Inference and Multivariate Analysis:

  1. Linear statistical models
  2. theory of least squares and analysis of variance
  3. Gauss- Markoff theory
  4. normal equations
  5. least squares estimates and their precision
  6. test of significance and interval estimates based on least squares theory in one- way,two-way and three-way classified data
  7. regression analysis
  8. linear regression
  9. curvilinear regression and orthogonal polynomials
  10. multiple regression
  11. multiple and partial correlations
  12. regression diagnostics and sensitivity analysis
  13. calibration problems
  14. estimation of variance and covariance components
  15. MINQUE theory
  16. multivariate normal distribution
  17. Mahalanobis
  18. D2 and Hotelling’s T2 statistics and their applications and properties
  19. discriminant analysis
  20. canonical correlations
  21. one-way MANOVA
  22. principal component analysis
  23. elements of factor analysis

Sampling Theory and Design of Experiments: 

  1. An outline of fixed-population and superpopulation approaches,
  2. distinctive features of finite population sampling
  3. probability sampling designs
  4. simple random sampling with and without replacement
  5. stratified random sampling
  6. systematic sampling and its efficacy for structural populations
  7. cluster sampling
  8. two-stage and multi-stage sampling
  9. ratio and regression
  10. methods of estimation involving one or more auxiliary variables
  11. two-phase sampling
  12. probability proportional to size sampling with and without replacement the Hansen-Hurwitz and the Horvitz-Thompson estimator
  13. nonnegative variance estimation with reference to the Horvitz-Thompson estimators non-sampling errors
  14. Warner’s randomised response technique for sensitive characteristics.
  15. Fixed effects model (two-way classification) random and mixed effects models (two-way classification with equal number of observation per cell), CRD, RBD,LSD and their analysis, incomplete block designs, concepts of orthogonality and balance, BIBD, missing plot technique, factorial designs: 2n, 32 and 33, confounding in factorial experiments, splitplot and simple lattice designs.

Paper – II

I. Industrial Statistics: 

  1. Process and product control
  2. general theory of control charts
  3. different types of control charts for variables and attributes, X, R, s, p, np and c
  4. charts
  5. cumulative sum chart
  6. V-mask
  7. single, double, multiple and sequential sampling plans for attributes
  8. OC, ASN, AQQ and ATI curves
  9. concepts of producer’s and consumer’s risks
  10. AQL
  11. LTPD and AOQL
  12. sampling plans for variables
  13. use of Dodge-Roming and Military Standard tables
  14. Concepts of reliability
  15. maintainability and availability
  16. reliability of series and parallel systems and other simple configurations
  17. renewal density and renewal function
  18. survival models (exponential, Weibull, lognormal, Rayleigh, and bath-tub)
  19. different types of redundancy and use of redundancy in reliability improvement
  20. Problems in lifetesting censored and truncated experiments for exponential models.

II. Optimization Techniques:

  1. Different types of models in Operational Research
  2. their construction and general methods of solution
  3. simulation and Monte-Carlo methods
  4. the structure and formulation of linear programming (LP) problem
  5. simple LP model and its graphical solution
  6. the simplex procedure
  7. the two-phase method and the Mtechnique with artificial variables
  8. the duality theory of LP and its economic interpretation, sensitivity analysis, transportation and assignment problems
  9. rectangular games
  10. two-person zero- sum games
  11. method of solution (graphical and algebraic).
  12. Replacement of failing or deteriorating items
  13. group and individual replacement policies
  14. concept of scientific inventory management
  15. analytical structure of inventory problems
  16. simple models with deterministic and stochastic demand with and without lead time
  17. storage models with particular reference to dam type.
  18. Homogeneous discrete-time Markov chains
  19. transition probability matrix
  20. classification of states and ergodic theorems
  21. homogeneous continuoustime Markov chains
  22. Poisson process
  23. elements of queuing theory
  24. M/M/1, M/M/K, G/M/1 and M/G/1 queues
  25. Solution of statistical problems on computers using well-known statistical software packages like SPSS.

III. Quantitative Economics and Official Statistics:

  1. Determination of trend, seasonal and cyclical components,
  2. Box-Jenkins method
  3. tests for stationery of series
  4. ARIMA models and determination of orders of autoregressive and moving average components, forecasting.
  5. Commonly used index numbers
  6. Laspeyre’s, Paashe’s and Fisher’s ideal Index numbers
  7. chain-base index numbers
  8. uses and limitations of index number
  9. index number of wholesale prices
  10. consumer price index number
  11. index numbers of agricultural and industrial production
  12. test for index numbers like proportionality test
  13. timereversal test
  14. factor-reversal test
  15. circular test and dimensional invariance test
  16. General linear model
  17. ordinary least squares and generalised least squares methods of estimation
  18. problem of multicollinearity
  19. consequences and solutions of multi-collinearity
  20. autocorrelation and its consequences
  21. heteroscedasticity of disturbances and its testing
  22. test for independence of disturbances
  23. Zellner’s seemingly unrelated regression equation model and its estimation
  24. concept ofstructure and model for simultaneousequations
  25. problem of identification-rank and order conditions of identifiability
  26. twostageleast squares method of estimation
  27. Present official statistical system in India relating to population
  28. Agriculture
  29. industrial production
  30. trade and prices
  31. methods of collection of official statistics
  32. their reliability and limitation and the principal publications containing such statistics various official agencies responsible for data collection and their main functions.

IV. Demography and Psychometry: 

  1. Demographic data from census, registration
  2. NSS and other surveys, and their limitation and uses
  3. Definition
  4. construction and uses of vital rates and ratios
  5. measures of fertility
  6. reproduction rates, morbidity rate
  7. standardized death rate
  8. complete and abridged life tables
  9. construction of life tables from vital statistics and census returns
  10. uses of life tables
  11. logistic and other population growth curve
  12. fitting a logistic curve
  13. population projection
  14. stable population theory
  15. uses of stable population
  16. quasi-stable population techniques in estimation of demographic parameters
  17. morbidity and its measurement
  18. standard classification by cause of death
  19. health surveys and use of hospital statistics.
  20. Method of standardisation of scales and tests
  21. Z-scores, standard scores
  22. Tscores, percentile scores
  23. intelligence quotient and its measurement and uses
  24. validity of test scores and its determination
  25. use of factor analysis and path analysis in psychometry

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