Objective
To enable the students to gain understanding of mathematical and statistical techniques as are applicable to commerce, industry, business and economic fields.
To make students competent to cope with the increasing importance and utility of Statistics in Computer Science, Operational Research, Quality Control etc.
Course Contents :
Unit I : Probability Distributions : 16%
Binomial, Poisson & Hyper Geometric Distributions; their probability mass function and derivation of their means; Properties and uses of these distributions (Value of e-m to be given)
Unit II :
(A) Negative Binomial and Geometric Distributions : 9%
Probability mass functions of the distributions, their means and variances (only statement); their properties & uses.
(B) Normal Distribution : 8%
Idea of a continuous random variable; Probability density function, prosperities and uses of Normal Distribution; Conditions for approximation of Binomial Distribution to Normal Distribution, Use of normal tables.
Unit III : Statistical Quality Control : 17%
Meaning & Use of SQC in industry; Causes of variation in quality, Control limits, Theory of runs, Control charts for variables - X and R charts; Control charts for attributes -p, np and c charts; Drawing of these charts and interpretation of result.
Unit IV : Linear Programming : 17%
Elementary theory of convex sets, definition of general liner programming problem. (LPP), formulation of LPP, examples of LPP, Problems occurring in various fields, Graphical method of solving LPP, Formulation of Transportation Problem. as LPP; its initial basic feasible solution by North-West Corner rule, Matrix minima method and Vogel's approximation method.
Unit V : Business Applications of Derivatives : 16%
Mathematical functions of demand and supply, price elasticity of demand and supply; cost functions - average cost, marginal cost; Marginal revenue and average revenue and their relationship with elasticity of demand; Market equilibrium, monopoly and duopoly problems.
Unit VI :
(A) Partial Differentiation : 9%
Definition of partial derivative involving two variables only upto first and second order. Idea of linear homogeneous function; Euler's theorem (statement only) and its applications; Use of partial derivatives in problems relating to utility functions and cost minimization under constraints.
(B) Elements of Decision Theory : 8%
Basic structure of decisions, classical basis of pay-off matrix models, pay-off matrix under conditions of risk, expected value, maxi-min, maxi-max, Harwich and Laplace criteria, Expected Monetary Values (EMV.)
Reference Books
1. Hooda, R.P.: Statistics for Business and Economics; Macmillan, New Delhi
2. Lewin and Robin : Statistics for Management, Prentice Hall of India, New Delhi
3. Vohra, N.D. : Quantitative Techniques in Management; Tata McGraw Hill New Delhi.
4. Loomba and N.Paul; Linear Programming, Tata McGraw Hill, New Delhi
5. R.S.N. Pillai & Mrs. V. Bagavathi : Statistics, Sultan Chand & Sons, Delhi
6. Kapoor V. K. : Business Mathematics; Pitamber Publishing House.
7. Soni, R.S. : Business Mathematics; Pitamber Publishing House.
8. Grant, E.L. : Statistical Quality Control, McGraw Hill
9. Duncan A. J. : Quality Control and Industrial Statistics, Taraporewala and Sons.
10. Gass S.I. : Linear Programming Methods and Applications, McGraw Hill
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Structure of Question Paper (Total Marks - 70, Time : 3 Hours)
1. The syllabus of the question paper is divided into six units.
2 There must be two questions from each unit which are internally optional.
3. A question paper should be set in such a manner that it covers the whole syllabus.
4. Each question must carry at least two sub questions. Out of these sub questions at least one should be theoretical and other sub question(s) should be the example(S).
5. The question paper should give 30% to 35% and 65% to 70% weight age to theory and examples respectively.
Unit - 1 Integration : 16%
Integration as anti-derivative process; Standard forms; Methods of Integration - by substitution, by parts and by use of partial fractions; Definite integration, properties of definite integrals (without proof); Finding areas in simple cases; Simple applications of definite integrals in business and commerce.
Unit - 2
(A) Raw and Central Moments : 8%
Definition; Inter-relationship between Raw and Central moments (upto fourth order), ß1 and ß2 co-efficients (Numerical examples only); Idea of Moment Generating Function and its properties.
(B) Normal Distribution : 9%
Derivation of mean and variance; Moment Generating Function about origin and mean; Derivation of the following formulae : (1) µ2r = 1.3.5. ..... (2r-3)(2r-1)s2r (2) µ2r+1=0 Calculation of probabilities (Numerical examples only)
Unit -3 Binomial and Poisson Distributions : 17%
Derivation of Binomial & Poisson distributions; their first four raw and central moments & MGF about origin & mean; their recurrence relations between moments namely.
(i) µr+1 = þq (nr-µr-1 + dµr/dp)
(ii) µr+1 = m (rµr-1 + dµr/dp)
Calculation of probabilities (Numerical example only)
Unit - 4 Large Sample Tests : 17%
Meaning of parameter & statistic; Idea of statistical hypothesis (null & alternative hypothesis), level of significant and confidence interval. Application for the following types of tests. 1. Test for number of success & proportions. 2. Test for difference between two proportions. 3. Test for a mean. 4. Test for difference between two means. 5. Test for difference between two standard deviations.
Unit - 5 Small Sample Tests : 16%
Idea of degrees of freedom. Tests of significance based upon t and F statistics; their applications for testing: (1) Mean (2) Difference between two means (3) Variance; c2 test; Confidence intervals for the mean and variance of a normal population for given confidence co-efficient (say, 95% & 99%)
Unit - 6
(A) Assignment Problem : 5%
Formulation of the problem; Hungarian method of solving an assignment problem.
(B) Replacement Problem : 5%
Importance of replacement models; Replacement problems for items that deteriorate with time and value of money remaining constant.
(C) Theory of Games : 7%
2 x 2 game problem with and without saddle point;
Reference Books :
1. Introduction to mathematical statistics; S.P. Gupta.
2. Fundamentals of statistics; D.N. Elhance.
3. Modern Statistics for Business Decisions; L.R. Lapin.
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6. Mathematical Analysis for Economists; Allen R.G.D.
7. Business Statistics; Sancheti & Kapoor; Sultan Chand and Sons.
8. Statistics; Dr. B.N. Gupta.
9. Fundamentals of statistics Vol. I; Goon Gupta and Das Gupta.
10. Quantitative Techniques in Management : N.D. Vohra.
11. Linear Programming : Loomba and Paul, Tata McGraw Hill, Publishing Company Ltd., New Delhi.
Structure of Question Paper (Total Marks - 70, Time : 3 Hours) 1. The syllabus of the question paper is divided into six units. 2. There must be two questions from each unit which are internally optional. 3. A question paper should be set in such a manner that it covers the whole syllabus. 4. Each question must carry at least two sub question. Out of these sub questions at least one should be theoretical and other sub question (s) should be the example (s). 5. The question paper should give 30% to 35% and 65% to 70% weightage to theory and examples respectively.