STATISTICS SYLLABUS
Probability: Random experiment, sample space, event, algebra of events, probability on a
discrete sample space, basic theorems of probability and simple examples based theorem,
conditional, probability of an event, independent events, Bayer’s 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, coefficient,
distribution of a function of random variables. Bernouli, binomial, geometric, negative binomial,
hypergeometric, poisson, multinomial, uniform, beta, exponential, gamma, cauchy, normal,
longnormal and bivariate normal distributions, real life situations where these distributions
provide appropriate models, Chebyshev’s inequality, weak law or 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 example, 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.
Wal’s sequential probability ratio test, OC and ASN functions, application to binomial and
normal distributions. Loss function, risk function, mini max 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 three way
classifications, analysis of covariance in one and two way classifications, completely
randomized design, randomized block design, latin square design, missing plot technique, 2n
factorial design, total and partial confounding, 3^2 factorial experiments, split plot design and
balanced incomplete block design.
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