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CLICK HERE to DOWNLOAD: 22131 Downloads so far )Statistics Syllabus IFoS Main Exam, 2021, 2022, 2023
Paper I : Statistics for IFoS Mains Exam
Max. Marks: 200
Duration: 3 hours
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, Borel-Cantelli lemma, Chebyshev’s and Khinchine‘s weak
laws of large numbers, strong law of large numbers and kolmogorov’s theorems,
Glivenko-Cantelli theorem, probability generating function, characteristic function,
inversion theorem, Laplace transform, related uniqueness and continuity theorems,
determination of distribution by its moments. Linderberg and Levy forms of central
limit theorem, standard discrete and continuous probability distributions, their interrelations
and limiting cases, simple properties of finite Markov chains.
Statistical Inference
Consistency, unbiasedness, efficiency, sufficiency, minimal sufficiency, completeness,
ancillary statistic, 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 and severalparameter
family of distributions, minimum variance bound estimator and its
properties, modifications and extensions of Cramer-Rao inequality, Chapman-Robbins
inequality, Bhattacharyya’s bounds, estimation by methods of moments, maximum
likelihood, least squares, minimum chi-square and modified minimum chi-square,
properties of maximum likelihood and other estimators, idea of asymptotic efficiency,
idea of prior and posterior distributions, Bayes estimators.
Non-randomised and randomised tests, critical function, MP tests, Neyman-Pearson
lemma, UMP tests, monotone likelihood ratio, generalised Neyman-Pearson lemma,
similar and unbiased tests, UMPU tests for single and several-parameter families of
distributions, likelihood rotates and its large sample properties, chi-square goodness of
fit test and its asymptotic distribution.
Confidence bounds and its relation with tests, uniformly most accurate (UMA) and
UMA unbiased confidence bounds.
Kolmogorov’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, Wilcoxon-Mann-Whiltney test and median test, their consistency and
asymptotic normality.
Wald’s SPRT and its properties, OC and ASN functions, Wald’s fundamental identity,
sequential estimation.
Linear Inference and Multivariate Analysis
Linear statistical modesl, theory of least squares and analysis of variance, Gauss-
Markoff theory, normal equations, least squares estimates and their precision, test of
signficance 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, regression diagnostics and sensitivity analysis, calibration problems,
estimation of variance and covariance components, MINQUE theory, multivariate
normal distributin, Mahalanobis;’ D2 and Hotelling’s T2 statistics and their
applications and properties, discriminant analysis, canonical correlations, one-way
MANOVA, principal component analysis, elements of factor analysis.
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 for structural populations, 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, nonnegative
variance estimation with reference to the Horvitz-Thompson estimator, nonsampling
errors, Warner’s randomised response technique for sensitive characteristics.
Fixed effects model (two-way classification) random and mixed effects models (twoway
classification per cell), CRD, RBD, LSD and their analyses, incomplete block
designs, concepts of orthogonality and balance, BIBD, missing plot technique, factorial
designs : 2n, 32 and 33, confounding in factorial experiments, split-plot and simple
lattice designs.
Paper II : Statistics for IFoS Mains Exam
Max. Marks: 200
Duration: 3 hours
I. 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, Vmask,
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-Romig and Military Standard
tables.
Concepts of reliability, maintainability and availability, reliability of series and parallel
systems and other simple configurations, renewal density and renewal function,
survival models (exponential), Weibull, lognormal, Rayleigh, and bath-tub), different
types of redundancy and use of redundancy in reliability improvement, problems in
life-testing, censored and truncated experiments for exponential models.
II. Optimization Techniques
Different, types of models in Operational Research, their construction and general
methods of solution, simulation and Monte-Carlo methods, the structure and
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 algerbraic).
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 continous-time Markov chains, Poisson
process, elements of queueing 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.
III. Quantitative Economics and Official Statistics
Determination of trend, seasonal and cyclical components, Box-Jenkins method, tests
for stationery of series, ARIMA models and determination of orders of autoregressive
and moving average components, forecasting.
Commonly used index numbers-Laspeyre's, Paashe's and Fisher's ideal index numbers,
chain-base index number uses and limitations of index numbers, index number of
wholesale prices, consumer price index number, index numbers of agricultural and
industrial production, tests, for mdex numbers lve proportonality test, time-reversal
test, factor-reversal test, circular test and dimensional invariance test.
General linear model, ordinary least squares and generalised least squires methods of
estimation, problem of multicollineaity, consequences and solutions of
multicollinearity, autocorrelation and its consequences, heteroscedasticity of
disturbances and its testing, test for independence of disturbances, Zellner's seemingly
unrelated regression equation model and its estimation, concept of structure and model
for simultaneous equations, problem of identification-rank and order conditions of
identifiability, two-stage least squares 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 limitation and the principal publications containing such statistics, various official
agencies responsible for data collection and their main functions.
IV. Demography and Psychometry
Demographic data from census, registration, NSS and other surveys, and their
limitation 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 theory, uses of stable population and quasistable
population techniques in estimation of demographic parameters, morbidity and
its measurement, 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, intelligence quotient and its measurement and uses, validity of test
scores and its determination, use of factor analysis and path analysis in psychometry.
Recommended Textbooks:
Introductory Probability and Statistical Applications - Paul Meyer
An Introduction to Probability Theory & Mathematical Statistics - V K Rohtagi
Fundamentals of Statistics - A M Goon, M K Gupta and B Dass Gupta
An Outline of Statistical Theory - A M Goon, M K Gupta and B .Dass Gupta
Fundamentals of Mathematical Statistics - A C Gupta and V K Kapoor
Fundamentals of Applied Statistics - S C Gupta and V K Kapoor
Sampling Techniques - William G. Cochran
Sampling Theory of Surveys with applications - B. V Sukhatme & B V Sukhatme
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