Investigators Examination

Syllabus Of Investigators Examination

Statistics

Probability, Probability Distributions: Binomial, Poisson, Normal, Exponential. Compilation, classification, tabulation of statistical data, Graphical presentation of data. Measures of central tendency, measures of dispersion, measures of association and contingency, scatter diagram, correlation coefficient, rank correlation efficient and linear regression analysis (for two or more variables) excluding partial correlation coefficients. Concept of Population, random sample, parameters, statistics, sampling distribution of x, properties of estimators and estimation of confidence intervals.

Principles of sampling, simple random sampling, stratified sampling, systematic sampling, etc. Sampling and Non-sampling errors, type-I and type-II errors. Concepts of Hypothesis: Null and alternate. Testing of hypothesis for large samples as well as small samples including Chi-square tests (Z,t,F,X tests). Index Numbers, Time series analysis-components of variation and their estimation.

Economics

(A) General Economics

• Demand and Supply Analysis, including Laws and Interaction
• Production Function and Laws of Returns.
• Commodity Pricing-Characteristics of various Market Forms under such Market form
• Theory of Factor Pricing-Rent, Wage, Interest and profit.
• Theory of Employment-Classical and Neo-classical Approach.
• Keynesian Theory of Employment-Principle of Effective Importance of Investment, Relation between saving and Inv Effect and the process of Income Generation, Post Keynesia
• Nature and Functions of Money, Value of Money, Fluctuation Money-Inflation and Deflation, Monetary Policy, Index Numb
• International Trade-Free Trade and Protection, Theories Trade.
• Foreign Exchange-Determination of the rate of Exchange Parity Theory and Balance of Payment Theory.
• Public Finance-Nature, Scope and importance of Public Finance.
• Taxation-meaning, Classification and Principles of Taxation.
• Deficit Financing.
• Fiscal Policy.

(B) Indian Economics & General Statistics:

• Statistical Investigation-Meaning and Planning of investigation.
• Collection of data and editing of data.
• Types of sampling.
• Schedule and questionnaire.
• Presentation of data-Classification, tabulation, etc.
• Measures of Central Tendency.
• National Income and Accounting-Estimation of National National Income, Structural changes in the Indian Economy Income Data.
• Agricultural Sector - Agricultural Development during Planning Credit, Agricultural Price Policy, Rural Development Co-operative Raj.
• Industrial Policy and Industrial Development.
• Problems of Economic Development-Indian Planning-Objective and its evolution, Five Year Plans and Role of National Development.
• Profile of Human Resources-Population and Economic Development. Profile of India, Nature of Population Problem-Poverty, In Problem, Labour Problem, Population Control and Government
• New Economic Policy and Welfare Schemes.
• Indian Public Finance-Indian Revenue, Foreign Aid. "
• Indian Banking and Currency system

Mathematics

Algebra:

Algebra of sets, relations and functions, Inverse of a function, equivalence relation. The system of complex numbers, De Moivere's Theorem and its simple applications. Relation between roots and coefficients of a polynomial equation - Evaluation of symmetric function of roots of cubic and biquadratic equation.

Algebra of Matrices:

Determinants, Simple properties of determinants, multiplication of determinants of orders two and three. Singular and non-singular matrices. Inverse of a matrix, Rank of a matrix and application of matrices to the solution of linear equations (in three unknowns). Convergence of sequences, and series, tests of convergence of series with positive terms, Ration, Root and Gauss tests.

Analytical Geometry:

Straight lines, Circles, system of circles, parabola, ellipse and hyperbola in standard form and their elementary properties. Classification of curves second degree. Differential Equation: First order differential equation. Solution of Second and higher order linear differential equations with constant coefficients and simple applications.

Differential and Integral Calculus:

Limit, continuity and differentiability of functions, successive differentiation, derivatives of standard functions, Rolle's and Mean-value Theorems, Maclaurins and Taylor's series ( without proof) and their applications, maxim and minima of functions of one variables. Tangents and normals, curvature, Partial differentiation, Euler's theorem for omogeneous function, Tracing of curves. Standard methods of integration. Riemann's definition of definite integral, fundamental theorem of integral calculus, quadrate, rectification, volumes and surface area of solids of revolution.

Statistics:

Frequency distributions, Measures of central tendency, measures of dispersion, Skewness and kurtosis. Random variables and distribution function. Discrete distributions. Binomial and Poisson distribution. continuous distributions. Rectangular, Normal and exponential distributions. Principles of least squares, correlation and regression. Random Sampling, random numbers. Sampling of attributes. Large Sample tests for mean and proportion. Tests of significance, based on t, F and Chi square distributions.