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STATISTICS
B.A/B.Sc. IST Semester
Course No. SOS/STAT/UG/C-101
Core Course -
Credit 4
Core 1.1: Differential Calculus
Limit and Continuity (ɛ and δ definition), Types of discontinuities, Differentiability of
functions, Successive differentiation
Tangent and normals, Curvature, Asymptotes, Singular points, Rolle’s theorem, Mean value
theorem.
Books Recommended
1. H. Anton, I. Birens and S. Davis, Calculus, John Wiley and Sons, Inc., 2002.
2. G.B. Thomas and R.L. Finney, Calculus, Pearson Education, 2007.
Core 1.2: Descriptive Statistics and Probability Theory
Nature of Statistics, Uses of Statistics, Statistics in relation to other disciplines, Concepts of a
statistical population and sample from a population, quantitative and qualitative data, discrete
and continuous data, Presentation of data by tables and by diagram, frequency distribution for
discrete and continuous data, Graphical representation of a frequency distribution by
histogram and frequency polygon, cumulative frequency distributions (inclusive and
exclusive methods).
Measures of Central tendency: Mean, Median, Mode, Geometric Mean and Harmonic mean:
their properties.
Measures of Dispersion: Range, Quartile Deviation, Mean Deviation, Standard Deviation and
their properties, Coefficient of variation, Moments, Skewness and Kurtosis cumulants.
Bivariate data: Scatter diagram, principle of least-square and fitting of polynomaial and
exponential curves, Correlation and regression, Karl Pearson coefficient of correlation, Lines
of regression.
Random experiment, sample point and sample space, event, algebra of events, Definition of
Probability-classical, relative frequency and axiomatic approaches to probability, merits and
demerits of these approaches (only general ideas to be given). Theorem on probability,
conditional probability, independent events, Baye’s theorem and its applications.
Books Recommended
1. J.E. Freund, Mathematical Statistics with Applications, 7th Ed., Pearson Education,
2009.
2. A.M. Goon, M.K.GUPTA and B. Dasgupta, Fundamental of Statistics, Vol. 1, 8th Ed.,
World Press, Kolkata, 2005.
3. S.C Gupta and V.K. Kapoor, Fundamental of Mathematical Statistics, 11th Ed., Sultan
Chand and Sons, 2007.
4. R.V. Hogg, A.T. Craig and J.W. Mckean, Intoduction to Mathematical Statistics, 6th
Ed., Pearson Education, 2005.
5. A.M. Mood, F.A. Graybill and D.C. Boes, Introduction to the Theory of Statistics, 3rd
Ed., Tata McGraw Hill Publication, 2007.
Core 1.3: Linear Programming
Introduction to Operational Research and overview of O.R. modelling.
Introduction to Linear Programming Problem, Problem formulations, Graphical solution,
Theory of Simplex method, Duality in Linear Programming, Economics interpretation of
duality.
Assignment problem, Transportation problem and its mathematical formulation, northwest
corner method, Least cost method.
Books Recommended
1. G. Hadley, Linear Programming, Narosa, 2002.
2. Hamdy A. Taha, Operation Research- An Introduction to operation researchConcepts and Cases, 9th Ed., Tata McGraw Hill, 2010.
Practical – Credit 2
PRACTICAL/LAB.WORK:
List of Practical
1. Graphical representation of data.
2. Problems based on measure of central tendency.
3. Problems based on measure of dispersion.
4. Problems based on combined mean and variance and coefficient of variation.
5. Problems based on moments, skewness and kurtosis.
6. Fitting of polynomial, exponential curves.
7. Karl Pearson correlation coefficient.
8. Correlation coefficient for a bivarate frequency distribution.
9. Lines of regression, angle between lines and estimated values of variables.
10. Spearman rank correlation with and without ties.
11. Partial and multiple correlations.
12. Problem based on probability.
13. Problem based on Baye’s theorem.
14. Mathematical formulation of L.P.P and solving the problem using graphical method.
15. Simplex technique to solve L.P.P and reading dual solution from the optimal table.
16. Allocation problem using Transportation model.
17. Allocation problem using Assignment model.
18. Problem based on Northwest corner method.
STATISTICS
B.A/B.Sc. IInd Year
Paper I: Theoretical Statistics
Unit I: Estimation: Concepts of population and sample Criteria for a good estimator,
underbiasedness minimum variance, efficiency and consistency, Methods of Moment, Least
Squares and Maximum likelihood and their application of simple cases.
Unit II: Testing of Hypotheses: Null and Alternative hypotheses, simple and composite
hypotheses, two types of errors, level of significance, Concept of power function. Test for a
simple hypotheses against a simple alternative in the case of Binomial, Poisson and Normal
distribution.
Unit III: Test of significance: Large sample tests of mean, variance proportions and
correlation coefficient, simple properties of chisquare, Student’s and Snedecor’s F with
applications in test of significance.
Paper II: Analysis and Variance Design of Experiments
Unit I: Analysis of Variance: One way, and two way classifications.
Unit II: Design of experiment, Principle of experimental design completely randomized,
randomized block and Latin square designs with analysis.
Unit III: Sampling theory: Sampling versus, census, simple random sampling with and
without replacement: Estimation of Population mean and variance, Standard random
sampling and systematic sampling.
Paper III: Operation Research
Unit I: Decision theory: Decision making under conditions of certainty, decision making
under condition of uncertainty EMV and EOL criteria, EPPI and EVPI.
Unit II: Games theory: Competitive games existence of saddle point true and unpured
strategic solution of game with and without saddle points, criteria of dominance.
Unit III: Linear programming problems: Introduction of operation research and its
application formulation of LPP and its solution by graphical methods, formulation of dual a
LPP.
Practical: There will be practical based on the syllabus of B.A/B.Sc – II.
STATISTICS
B.A/B.Sc. IIIrd Year
Paper-1: Numerical Analysis
Unit 1:
Finite difference, difference operators, Newton’s forward and backward
interpolation formula interpolation with unequal interval arguments, Lagrange’s formulae,
Newton’s divided difference formula Striling’s and Bessel’s formula (without proof).
Unit II: Numerical differentiation, Numerical integration, trapezoidal rule, Simpson’s 1/3
and 3/8 rule and Welde’s rule (without proof).
Unit III: Pearsonian system of curves – Pearsonian differential equation, moments, Pearsons
type III, IV and X2 distribution.
Paper – II: Quality Control
Unit I: Process control: Use of control charts by attributes and by variables.
Unit II: Single, Double and sequential sampling plan by attributes, Producers risk,
consumers risk OC, ASN, ATI curves AOQ and AOQL.
Unit III: Sampling plan by variables known sigma, and unknown sigma, one-sided upper and
lower specification, with sided specification.
Paper – III: Demography
Unit I: Biological theories and hypothesis of fertility, Malthusian theory of population, pearl
and reed hypothesis, Herbert Spencer’s theory, Jouse De Castro’s hypothesis, Robert
Ardrey’s hypothesis, Analysis of food fertility link.
Unit II: Marxian theory of surplus population Dumont’s hypothesis, The Becker model of
fertility, Easterlin’s hypothesis, Development of transition theory, leading stage of population
profile of demographic explosion.
Unit III: Vital Statistics and Graduation formula crude and standardized death rate, General
fertility rateage specific fertility rate, Total fertility rate gross and net reproduction rate
elements of life table, Graduation of population data, logistic curve, fitting of logistic curve,
graduation of mortality rate, Makcham’s formula.
Practical: There will be practical based on the syllabus of B.A/B.Sc – III.