# PSC Chhattisgarh Prelims - Statistics Syllabus

Updated on: Apr 2, 2013

The syllabus of Statistics of PSC Chhattisgarh Prelim Exam is given in this section.

Classical and axiomatic definitions of probability. Simple theroems on probability with examples, conditional; probability, statistical independence. Bayes theorem. discrete and continuous random variables, probability mass function and probability density function,cumulative distribution function, joint, marginal and conditional probability distributions in case of two random variables, expectation moment, moment generating function. chebyshev's inequality Binomial, Poisson. Hypergeometric,Negative binomial , uniform, exponential, gamma, beta, normal and bivariate normal probability distributions, convergencein probability , weak law of large numbers; simple form of central limit theorem (without proof).

Compilation, classification, tabulation and diagrammatic representation of statistical data, measures of central tendency, dispersioin,skweness and kurtosis, measures of association and contingency, correlation and linear regression involving two variables, curve fitting, rank correlation.

Concept of a random sample and statistics, tests of significance based on t, f and x2 statistics.

Theory of estimation, unbiasedness, consistency, efficiency, sufficiency, Cramer-Rao inequality , methods of estimation-method of moments, maximum likelihood, least squares, properties of maximum likelihood estimators (without proof) simple problems of constructing confidence intervals. Testing of hypotheses, simple-and composite hypotheses , statistical tests, two kinds of error, best critical regions for simple hypotheses concerning one parameter.

Principles of sampling , frames and sampling units, sampling and non-sampling errors, simple random sampling stratified sampling, systematic sampling, designing of sample surveys.S

Analysis of variance with equal number of observations per cell in one, two and three way classification,s principles of experimental design, completely randomized design, randomized block design. latin square design, missing plot technique.

I. Probability (25 percent, weight)I. Probability (25 percent, weight)

Classical and axiomatic definitions of probability. Simple theroems on probability with examples, conditional; probability, statistical independence. Bayes theorem. discrete and continuous random variables, probability mass function and probability density function,cumulative distribution function, joint, marginal and conditional probability distributions in case of two random variables, expectation moment, moment generating function. chebyshev's inequality Binomial, Poisson. Hypergeometric,Negative binomial , uniform, exponential, gamma, beta, normal and bivariate normal probability distributions, convergencein probability , weak law of large numbers; simple form of central limit theorem (without proof).

**II. Statistical methods (25 percent weight)**Compilation, classification, tabulation and diagrammatic representation of statistical data, measures of central tendency, dispersioin,skweness and kurtosis, measures of association and contingency, correlation and linear regression involving two variables, curve fitting, rank correlation.

Concept of a random sample and statistics, tests of significance based on t, f and x2 statistics.

**III Statistical Inference ( 25 percent,weight)**Theory of estimation, unbiasedness, consistency, efficiency, sufficiency, Cramer-Rao inequality , methods of estimation-method of moments, maximum likelihood, least squares, properties of maximum likelihood estimators (without proof) simple problems of constructing confidence intervals. Testing of hypotheses, simple-and composite hypotheses , statistical tests, two kinds of error, best critical regions for simple hypotheses concerning one parameter.

**IV. Sampling theory and design of Experiments (25 percent, weight)**Principles of sampling , frames and sampling units, sampling and non-sampling errors, simple random sampling stratified sampling, systematic sampling, designing of sample surveys.S

Analysis of variance with equal number of observations per cell in one, two and three way classification,s principles of experimental design, completely randomized design, randomized block design. latin square design, missing plot technique.