SYLLABUS FOR UNION
PUBLIC SERVICE COMMISSION MAIN EXAMINATION
STATISTICS
PAPER
- I
1.
Probability:
Sample
space and events, probability measure and probability space, random variable as
a measurable function, distribution function of a random variable, discrete and
continuous-type random variable, probability mass function, probability density
function, vector-valued random variable, marginal and conditional
distributions, stochastic independence of
events
and of random variables, expectation and moments of a random variable,
conditional expectation, convergence of a sequence of random variable in distribution,
in probability, in p-th mean and almost everywhere, their criteria and
inter-relations, Chebyshev’s inequality
and
Khintchine‘s weak law of large numbers, strong law of large numbers and
Kolmogoroff’s theorems, probability generating function, moment generating
function, characteristic function, inversion theorem, Linderberg and Levy forms
of central limit theorem, standard discrete and continuous probability
distributions.
2.
Statistical Inference:
Consistency,
unbiasedness, efficiency, sufficiency, completeness, ancillary statistics,
factorization theorem, exponential family of distribution and its properties,
uniformly minimum variance unbiased (UMVU) estimation, Rao-Blackwell and
Lehmann-Scheffe theorems, Cramer- Rao inequality for single parameter.
Estimation by methods of moments, maximum
likelihood,
least squares, minimum chi-square and modified minimum chisquare, properties of
maximum likelihood and other estimators, asymptotic efficiency, prior and
posterior distributions, loss function,
risk function, and minimax estimator. Bayes estimators. Non-randomised and
randomised tests, critical function, MP tests, Neyman- Pearson lemma, UMP
tests, monotone likelihood ratio, similar and unbiased tests, UMPU tests for
single parameter likelihood ratio test and its asymptotic distribution.
Confidence bounds and its relation with tests. Kolmogoroff’s test for goodness
of fit and its consistency, sign test and its optimality. Wilcoxon signed-ranks
test and its consistency, Kolmogorov-Smirnov twosample
test,
run test, Wilcoxon-Mann- Whitney test and median test, their consistency and
asymptotic normality. Wald’s SPRT and its properties, OC and ASN functions for
tests regarding parameters for Bernoulli, Poisson, normal and exponential
distributions. Wald’s fundamental identity.
3.
Linear Inference and Multivariate Analysis:
Linear
statistical models’, theory of least squares and analysis of variance, Gauss-
Markoff theory, normal equations, least squares estimates and their precision,
test of significance and interval estimates based on least squares theory in
oneway, two-way and three-way classified data, regression analysis, linear
regression, curvilinear regression and orthogonal
polynomials,
multiple regression, multiple and partial correlations, estimation of variance
and covariance components, multivariate normal distribution, Mahalanobis-D2 and
Hotelling’s T2 statistics and their applications and properties, discriminant
analysis, canonical correlations,
principal
component analysis.
4.
Sampling Theory and Design of Experiments:
An
outline of fixed-population and super population approaches, distinctive
features of finite population sampling, probability sampling designs, simple
random sampling with and without replacement, stratified random sampling, systematic
sampling and its efficacy , cluster sampling, two-stage and multi-stage
sampling, ratio and regression methods of estimation involving one or more
auxiliary variables, two-phase sampling, probability proportional to size
sampling with and without replacement, the Hansen-Hurwitz and the
Horvitz-Thompson estimators, non-negative variance estimation with reference to
the Horvitz-Thompson estimator, non-sampling errors. Fixed effects model
(two-way classification) random and mixed effects models (two-way
classification with equal observation per cell), CRD, RBD, LSD and their
analyses, incomplete block designs, concepts of orthogonality and balance,
BIBD,
missing plot technique, factorial experiments and 2n and 32, confounding in
factorial experiments, split-plot and simple lattice designs, transformation of
data Duncan’s multiple range test.
PAPER
- II
1.
Industrial Statistics:
Process
and product control, general theory of control charts, different types of
control charts for variables and attributes, X, R, s, p, np and c charts,
cumulative sum chart. Single, double, multiple and sequential sampling plans
for attributes, OC, ASN, AOQ and ATI curves, concepts of producer’s and
consumer’s risks, AQL, LTPD and AOQL, Sampling plans for variables, Use of Dodge-Roming
tables. Concept of reliability, failure rate and reliability functions,
reliability of series and parallel systems and other simple configurations,
renewal density and renewal function, Failure models: exponential, Weibull,
normal, lognormal. Problems in life testing, censored and truncated experiments
for exponential models.
2.
Optimization Techniques:
Different
types of models in Operations Research, their construction and general methods
of solution, simulation and Monte-Carlo methods formulation of linear
programming (LP) problem, simple LP model and its graphical solution, the
simplex procedure, the two-phase
method
and the M-technique with artificial variables, the duality theory of LP and its
economic interpretation, sensitivity analysis, transportation and assignment
problems, rectangular games, two-person zero-sum games, methods of solution
(graphical and algebraic). Replacement of failing or deteriorating items, group
and individual replacement
policies,
concept of scientific inventory management and analytical structure of
inventory problems, simple models with deterministic and stochastic demand with
and without lead time, storage models with particular reference to dam type.
Homogeneous discrete-time Markov chains, transition probability matrix,
classification of states and ergodic theorems,
homogeneous
continuous-time Markov chains, Poisson process, elements of queuing theory,
M/M/1, M/M/K, G/M/1 and M/G/1 queues. Solution of statistical problems on
computers using well-known statistical software packages like SPSS.
3.
Quantitative Economics and Official Statistics:
Determination
of trend, seasonal and cyclical components, Box-Jenkins method, tests for
stationary series, ARIMA models and determination of orders of autoregressive
and moving average components, forecasting. Commonly used index numbers-
Laspeyre’s, Paasche’s and Fisher’s ideal index numbers, chain-base index
number, uses and limitations of index numbers, index number of wholesale
prices, consumer prices, agricultural production
and
industrial production, test for index numbers - proportionality, time-reversal,
factor-reversal and circular . General linear model, ordinary least square and
generalized least squares methods of estimation, problem of multicollinearity,
consequences and solutions
of
multicollinearity, autocorrelation and its consequences, hetero scedasticity of
disturbances and its testing, test for independence of disturbances, concept of
structure and model for simultaneous equations, problem of identification-rank
and order conditions of identifiability, twostage least square method of
estimation. Present official statistical system in India relating to
population, agriculture, industrial production, trade and prices, methods of
collection of official statistics, their reliability and limitations, principal
publications containing such statistics, various official agencies responsible
for data collection and their main functions.
4.
Demography and Psychometry:
Demographic
data from census, registration, NSS other surveys, their limitations and uses,
definition, construction and uses of vital rates and ratios, measures of
fertility, reproduction rates, morbidity rate, standardized death rate,
complete and abridged life tables, construction of life tables from vital statistics
and census returns, uses of life tables, logistic and other population growth
curves, fitting a logistic curve, population projection, stable
population,
quasi-stable population, techniques in estimation of demographic parameters,
standard classification by cause of death, health surveys and use of hospital
statistics.
Methods
of standardisation of scales and tests, Z-scores, standard scores, Tscores,
percentile scores, intelligence quotient and its measurement and uses, validity
and reliability of test scores and its determination, use of factor analysis
and path analysis in psychometry.
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