Punjab Public Service Commission (PPSC)
Preliminary Examination Syllabus - Statistics
Probability :
Random experiment, sample space, event, algebra of events,
probability on a discrete sample space, basic theorems of probability and simple
examples based thereon, conditionalprobability of an event, independent events,
Bayes’ theorem and its application, discrete and continuous random variables and
their distributions, expectation, moments, moment generating function, joint
distribution of two or more random variables, marginal and conditional
distributions, independence of random variables, covariance, correlation,
co-efficient, distribution of function of random variables. Bernoulli, binomial,
geometric, negative binomial, hypergeometric, Poisson, multinomial, uniform,
beta, exponential, gamma, Cauchy, normal, lognormal and bivariate normal
distributions, real-life situations where these distributions provide
appropriate models, Chebyshev’s inequality, weak law of large numbers and
central limit theorem for independent and identically distributed random
variables with finite variance and their simple applications.
Statistical Methods :
Concept of a statistical population and a sample, types of
data, presentation and summarization of data, measures of central tendency,
dispersion, skewness and kurtosis, measures of association and contingency,
correlation, rank correlation, intraclass correlation, correlation ratio, simple
and multiple linear regression, multiple and partial correlations (involving
three variables only),curve-fitting and principle of least squares, concepts of
random sample, parameter and statistic, Z, X2, t and F statistics and their
properties and applications, distributions of sample range and median (for
continuous distributions only), censored sampling (concept and illustrations).
Statistical Inference :
Unbiasedness, consistency, efficiency, sufficiency,
Completeness, minimum variance unbiased estimation, Rao-Blackwell theorem,
Lehmann-Scheffe theorem, Cramer-Rao inequality and minimum variance bound
estimator, moments, maximum likelihood, least squares and minimum chisquare
methods of estimation, properties of maximum likelihood and other estimators,
idea of a random interval, confidence intervals for the Parameters of standard
distributions, shortest confidence intervals, large-sample confidence intervals.
Simple and composite hypotheses, two kinds of errors, level of significance,
size and power of a test, desirable properties of a good test, most powerful
test, Neyman-Pearson lemma and its use in simple examples, uniformly most
powerful test, likelihood ratio test and its properties and applications.
Chi-square test, sign test, Wald-Wolfowitz runs test, run
test for randomness, median test, Wilcoxon test and Wilcoxon-Mann-Whitney test.
Wald’s sequential probability ratio test, OC and ASN
functions, application to binomial and normal distributions.
Loss function, risk function, minimax and Bayes rules.
Sampling Theory and Design of Experiments :
Complete enumeration vs. sampling, need for sampling, basic
concepts in sampling, designing large-scale sample surveys, sampling and
non-sampling errors, simple random sampling, properties of a good estimator,
estimation of sample size, stratified random sampling, systematic sampling,
cluster sampling, ratio and regression methods of estimation under simple and
stratified random sampling, double sampling for ratio and regression methods of
estimation, two-stage sampling with equal-size first-stage units.
Analysis of variance with equal number of observations per
cell in one, two and threeway classifications, analysis of covariance in one and
two-way classifications, basic priniciples of experimental designs, completely
randomized design, randomized block design, latin square design, missing plot
technique, 22 factorial design, total and partial confounding, 32 factorial
experiments, split-plot design and balanced incomplete block design.
