UPSC  Syllabus  Statistics   

Examination Syllabus  Subject : Statistics
Probability
Random experiment, sample space, event, algebra of events, probability on a discrete sample space, basic theorems of probability and simple examples based there on, conditional probability 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, coefficient, distribution of function of random variables. Bernoulli, binomial, geometric, negative binomial, hypergeometric, Poisson, multinomial, uniform, beta, exponential, gamma, Cauchy, normal, longnormal and bivariate normal distributions, reallife 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), curvefitting 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, RaoBlackwell theorem, LehmannScheffe theorem, CramerRao 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 paramters of standard distributions, shortest confidence intervals, largesample 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, NeymanPearson lemma and its use in simple example, uniformly most powerful test, likelihood ratio test and its properties and applications.
Chisquare test, sign test, WaldWolfowitz runs test, run test for randomness, median test, Wilcoxon test and WilcoxonMannWhitney test.
Wal'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 largescale sample surveys, sampling and nonsampling 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 estimaton under simple and stratified random sampling, double sampling for ratio and regression methods of estimation, twostage sampling with equalsize firststage units.
Analysis of variance with equal number of observations per cell in one, two and threeway classifications, analysis of covariance in one and twoway classifications, basic priniciples of experimental designs, completely randomized design, randomized block design, latin square design, missing plot technique, 2n factorial design, total and partial confounding, 32 factorial experiments, splitplot design and balanced incomplete block design.
