1. Topiccs-1 Statistical regularity of change phenomes. Frequency approach to probability classical definition of probability, Idealized exiometic approach to probability, random experiment, outcome sample space, events, exiomatic definition of probability. Algebra of events union. Intersection and complementation, conditional probability. Bayes theorem, Addition and multiplication rule of probability Independent events.
2. Topic-2 (a) Definition of random variables and its distribution, Desete and continuous random variables, Distribution function of continuous and discrete random variables and their properties. Topic-2 (b) Mathematical expectation, moments, moment generation function-Raw and central factorial moments and cumulates with their relationship up to fourth order, mode, Quartiles, coefficient of variation, measures of skewness and kurtosis.
3 Topic -3 Standard univariate distributions :
4 Hyper geometric, Binomial, poison, uniform, normal, gamma and beta distributions with their properties.
5 Topic-4 Sampling distribution. Sampling distribution of sample mean from binomial, poison and normal sampling distribution of the difference of the difference of two sample means from independent normal populations concept of Std. error of sample moments, statement of central limit theorem and its in asymptotic distribution of sample mean.
1 Topic-1 Sample survey : Sampling verses
2 complete enumeration, method of data collection and their compilation. Nature of survey (single & respectitive) different steps in large scale sample, biases in serveys types of population and types of samplimy importence of population census, Method of population census and study of last censues. Topic-2 Vital Statistic : Raesof vital events, Measurement of mortality curde death rate, specific death rate, standardised death rate, measurement of fertility : crude birth rate, general fertility rate, Age specific fertility rate, Total fertility rate, gross and net reproduction rate-concepts of life, tables and its uses, measurement of population groth.
3. Topic-3 (a) Index mumbers : Construction & use of index number, weighted index numbers, paasche Laspeyre, Fisher, Edgeworht-marshall formula for index numbers, test of index numbers, chain index numbers, Constructon of cost of living index numbers and whole sale price index numbers.
4. Topic-3 (b) Time series : Component of time series measurement of trend by method of moving averages and mathematical curves (upto second degree )
Topic-3 (c) National income : Definitation of national income, method of estimation of national income, distribution of income by SBC-Pareto's Law of income distribution and Lorenz Curves of Concentration.
5. Topic-3 (d) Mathematical Economics : Formulation of demand & supply functions, market equilibrium, determination of demand & supply cost cuves from time series data & utility function. Elastricity of demand and and supply and cost function. optimiration of revenue for a given demand law, use of elasticity in classifying goods into necessiaties & luxuries, problem of monopoly. Total - 5 There must be two questions from each unit which are
1. Topics-1 (a) Correlation : General concept of bivariate marginal and conditional distributions, covariances. Product moment correlation coefficient spearman's Rank correlation coefficient. Independence and uncorrelatedness of random variables.
2. Topic-1 (b) Regression : concept of regression error in regression, fitting of linear and quadratic curve and curves which are reducible to linear forms by method of leastsquare. Partial and multiple regression, multiple and partial correlation coefficient and their relationship. Topic-2 Sample test ; Idea of a null hypothesis, Alternative hypothesis, Level of significance and degree of freedom, chi-square. T and F tests and their use in the tests of significance cinccerning mean, Variances, total,partial & multiple correlation coefficients. Topics-3 Large sample tests : Contingency tables and association of attributes, chi-square test in testing of independence of attributes in contingency tables and goodness of fit, Test for sample proportion, Fishers-z-transformation and its use in testing significance of total and partial correlation coefficents.
4. Topic-4 Sampling techinques : Dr awing of random samples with and without replacement from a finite population, simple random, sampling, derivation of variance sample mean, random sampling for proportion, estimation of sample size and population total, startified random sampling and derivation of variance of startified sample mean. Total 5 There must be two questions from each unit which are internal optional.
