Subject: Statistics

PROBABILITY (25 PER CENT WEIGHT) :

Classical and axiomatic definitions of probability, simple thermos on probability with examples, conditional probability, statistical independence Bayes’ theorem,
Discrete and continuous random variables probability mass function and probability density function, cumulative distributions function, joint marginal and conditional probability distributions of two variables, functions of one and two random variables moments, moment generating function chebichev’s inequality, Binominal, Poison Hyper geometric Negative Bi-nominal, Uniform, exponential gamma, ‘beta, normal and bivariate normal probability distributions Convergence in probability weak law of large numbers, simple form of central limit theorem.

STATISTICAL METHODS (25 PERCENT WEIGHT) :

Compilation, classification, tabulation and diagrammatic representation of statisical data, measures of central tendency, dispersion, skewness and kurtosis measures of association and contingency correlation and incur regression involving two variables, correlation ration, curve fitting. Concept of a random sample and statistics, sampling distributing of X, X2 , T and F statistics, their properties, estimation and tests of significance based on them, order statistics and their sampling distributions in case of uniform and exponential parent distribution.

STATISTICAL INFERENCE (25 PERCENT WEIGHT) :

Theory of estimation, unbiased ness, consistency, efficiency, sufficiency, Grammar, Lower bound, best linear unbiased estimates, methods of estimation, methods moments, maximum likelihood, least squares, minimum X2 properties of maximum likelihood estimators (without proof), simple problems of constructing confidence intervals. Testing of hypothesis, and composite hypotheses, Statistical tests. two kinds of error, optional critical regions for simple hypothesis concerning one parameter. likelihood ratio tests, tests for the parameters of binomial, Poison, Uniform, exponential and normal distributions. Chi-square test, sign test, run test, medium test, Wilcox on test rank correlation methods.

SAMPLING THEORY AND DESIGN OF EXPERIMENTS (25% WEIGHT):

Principles of campling, frame and sampling units. sampling and non sampling errors, simple random sampling, stratified sampling, cluster sampling, systematic sampling, ratio and regression estimates, designing of sample surveys with reference to recent large scale surveys in India. Analysis of variance with equal number of observations per cell in one, two and three way classifications, transformations to stabilize variance. Principles of experimental design, completely randomized design, Randomized block design, Latin square design, missing plot technique, factorial experiments with confounding in design balanced incomplete block designs.

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