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21. STATISTICS :
PAPER I
Note-Attempt any five questions choosing at least two from each section. Four questions of equal
weight age be set in each section.
SECTION-l
Statistical Methods- Measures of centraltendency, dispersion, skewness and kurtosis, measures of association
and contingency, correlation and regression, partial and multiple correlation, rank correlation, curve fitting.
Probability- Sample space and events. Theorems on probability, statistical independence, Bayes theorem,
discrete and continuous random variables, probability mass function, probability density function, distribution function,
bivariate distribution, marginal and conditional distributions, expectation moments, moment generating,
function, Chebyshev's inequality, Binomial, Poisson, Hypergeo-metric. Negative binomial, uniform, exponential,
gamma, Beta, normal and bivariate normal probability distributions. Convergence in probability, weak law of large
numbers and simple form of central limit theorem (without proof)
SECTION-II
Statistical Inference- Requirements of good estimate-unbiasedness, consistency, sufficiency and
efficiency, Cramer -Rao inequality. Methods of estimation- method of moments, method of maximum likelihood.Properties of maximum likelihood estimates (Without proof)
confidence intervals.
Simple and composite hypotheses, statistical tests, critical region, two kinds of error, Neyman Pearson lemma
and its applications for constructing tests for one parameter.
Tests of significance based on F and chi-square (x2) statistics.
PAPER-II
Attempt any five questions choosing at least two from each section. Four questions of equal
weight age be set in each section.
SECTION-I
Sampling techniques -Nature and scope of sampling, simple random sampling .estimation of ratio and proportion.
stratified sampling, systematic sampling, sampling and non-sampling errors, planning and organisation of sample
service.
Design of Experiments- Analysis of variance for one Way, two way and three way classifications.
Principles of
experimental designs, completely randomized design, Randomized block design.Latin square design, missing plot
techniques (one missing observation).
SECTION. II
Index Numbers- Definition, construction, interpretation and limitations of index numbers Lespoyre,
Passche, Edge -Wonh-Marshall and Fisher index numbers. tests for index numbers and construction of cost of living
index number.
Statistical Quality Control :
Concepts of quality and meaning of control .Different types of control charts (X,R,-P,n,p,c) sampling inspection versus 100% inspection, single
sequencial sampling plan , O.C.,A.S.N. and T.I. curves. Concepts of
producer's and consumers risk. -
Vital Statistics:-
Vital rates and ratios, crude death and birth rates. specific birth and death rates, standardized death rate, infant
mortality rate, life table description and uses. General fertility rate, total fertility rate. Gross and net reproduction
rates. Indian census.
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