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(Syllabus) Punjab PSC (Main) : Combined State Civil Services Exam - Statistics
Punjab Public Service Commission
SYLLABI FOR THE EXAMINATION PART B MAIN EXAM
STATISTICS
PART-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 chi-square, 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 two-sample test, run
test, WilcoxonMann-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 one-way, 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 zerosum 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, chainbase 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, heteroscedasticity 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, two-stage 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 funcstions.
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,
T-scores, percentile
scores, inteligence quotient and its measurement and uses validity and
reliability of test scores and
its determination, use of factor analysis and path analysis in psychometry.