# Statistics Syllabus PPSC Exam

Updated on: Mar 5, 2013

**Section I**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 variables, 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 probability, Chebyshevs weak laws of large numbers, probability generating function, characteristic function, inversion theorem, Lindberg-Levy central limit theorem, standard discrete and continuous probability distributions, their inter-relations.

**Section II****Statistical Inference :**Consistency, unbiasedness, efficiency, sufficiency, minimal sufficiency, completeness, ancillary statistics, factorization theorem, exponential family of distributions and its properties, uniformly minimum variance unbiased (UMVU) estimation, Rao-Blackwell and Lehmann-Scheffe theorems, Cramer-Rao inequality for single parameter family of distributions, minimum variance bound estimator and its properties, estimation by methods of moments, maximum likelihood, least squares, 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, 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.

Kolmogorovs test for goodness of fit, sign test, Wilcoxon signed-rank test, Kolmogorov-Smirnov two-sample test, run test, Wilcoxon-Mann-Whitney test and median test. Walds SPRT and its properties, OC and ASN functions, Walds fundamental identity.

**Section III****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, multiple regression, multiple and partial correlations. Multivariate normal distribution, Mahalanobis-D2 and Hotellings T2 statistics and their applications and properties.

**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 sampling, ratio and regression, methods of estimation involving one auxiliary variables, probability proportional to size sampling with and without replacement, the Hansen-Hurwitz and the Horvitz-Thompson estimators, non-sampling errors, 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 designs.

**Section IV****Industrial Statistics :**Process and product control, general theory of control charts, different types of control charts for variables and attributes, ?, R, s, p, np and c charts. Single, double, and sequential sampling plans for attributes, OC, ASN, AOQ and ATI curves, concepts of producers and consumers risk, AQL, LTPD and AOQL, sampling plans for variables, use of Dodge-Romig and Military Standard tables.

**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, transportation and assignment problems, rectangular games, two-person zero-sum games, methods of solution (graphical and algebraic).**

Optimization Techniques :

Optimization Techniques :

**Quantiative Economics :**Definition of time series, the four components of a time series, measurement of secular trend by the method of moving averages and fitting of mathematical curves, measurement of seasonal fluctuations by ratio to moving average, ratio to trend and link relative methods, measurement of cyclical fluctuations (excluding periodogram analysis).

Commonly used index numbers-Laspeyres, Passches and Fishers ideal index numbers, chain-base index numbers, uses and limitations of index numbers, index number of wholesale prices, consumer price index number, index numbers of agricultural and industrial production, tests for index numbers like, time-reversal test, factor-reversal test and circular test.

**Demography :**Demographic data from census, registration, NSS and other surveys and 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 cuves, fifting a logistic curve, population projection.