# ICMAB

## 003. QUANTITATIVE TECHNEQUES: (BUSINESS MATHEMATICS AND STATISTICS)

### Course Objective

This course is designed to achieve the following objectives. These are to:
a. explain and demonstrate the use of basic mathematics including formula and ratios
b.  explain and apply financial mathematical techniques
c. identify reasonableness in the calculation of answers
d.  how to formulate a problem in mathematical terms, solve the problem and be able to interpret the results
e.  understand the basic concepts of statistics
f. equip themselves with statistical tools for analyzing business information
g.  identify and apply techniques for summarizing and analyzing data
h. explain and demonstrate techniques used forforecasting and drawing inference
i. explain and demonstrate the use of probability where risk and uncertainty exist
j.  understand the formulation of hypothesis in the area of business and interpret their results.

A. Business Mathematics (Marks - 50)

Exponential, Permutation & Combination-Weight-15%

003.01 Set Theory
Types of sets, Venn diagram, Operations of sets, Number of elements in a finite set. Application of set theory in problems related to probability calculation.

003.02 Mathematics of Finance
Interest and its computation - simple interest, compound interest, power of compound growth; Single payment computations - compound amount, present value; Annuities and their future value- sum of an annuity, determining the size of an annuity; annuities and their present value-present value of an annuity, determining the size of an annuity, mortgages; Cost-benefit analysis, discounted cash flow, NPV, IRR.

003.03 Linear and Quadratic Equations
Linear Equations - characteristics, graphing two-variable equations, Slope-intercept form, Slope and intercept, Slope and one point, Two points formulation. Systems of equalities and non-equalities. Solutions of simultaneous equations. Linear equations applications - Linear cost functions, linear revenue functions - linear profit functions, Break-even analysis. Quadratic Equations - characteristics, graphical representation, y intercept, x intercept, determining roots by factoring, determining roots by using quadratic formula, location of vertex. Quadratic application-Quadratic revenue function, quadratic supply function, Quadratic demand function, supply-demand equilibrium.

Exponential, Permutation & Combination-Weight-10%

003.04 Exponential and Logarithmic Functions
Exponential function - General characteristics, Characteristics of function f(x) = bx where b>1, Characteristics of f(x) = bx where 0<b<1, Base-e exponential function. Application of Exponential function- Continuous compounding, decay functions.
Logarithms and logarithmic functions - Properties, Common and natural Logarithms, Antilogarithms, Applications in compounding, half life, etc.

003.05 Permutations and Combinations
Difference between permutation and combination. Calculation of permutation and combination. Emphasis should be on their use in calculation of probability problems.

Trigonometry &  Calculus-Weight-15%

003.06 Trigonometry
Measurement of angles, trigonometric ratios, Trigonometrical functions, Relations between trigonometrical functions, Signs of trigonometric functions, Trigonometric functions of standard angles.

003.07 Calculus
Differential Calculus: Rules of differentiation, Successive differentiation, partial differentiation. Identification of Maxima and Minima - relative extrema, critical points, first-derivative test, second-derivative test, (when first-derivative test fails). Application of differential calculus - Revenue application, Cost application, Profit application, Marginal approach to Profit maximization.
Integral Calculus: Anti-derivative concept, rules of integration, Integration by parts, Integration by partial fractions, Definite integrals - evaluating definite integrals, properties, areas between a function and the x axis, finding areas between curves. Application of integral calculus-Revenue application, Cost application, Profit maximization application.

Matrix – Weight- 10%

003.08 Matrix Algebra
Vector, Square matrices, Transpose of Matrix. Matrix Operations - Addition, Subtraction, Scalar Multiplication, Matrix Multiplication, Representation of an equation and systems of equations. Determinant - 2 x 2 determinant, 3 x 3 determinant, methods of cofactors, properties of determinants. Inverse of a Matrix - Determining the inverse, Finding the inverse using cofactor, inverse of systems of equations. Applications of Matrix Algebra - Production planning, Equilibrium conditions, Input-output analysis, Network analysis.

Business Statistics (Marks-50)
Descriptive Statistics-Weight- 20%
003.01 Introduction
Meaning, scope and importance of Statistics.

003.02 Organization and Presentation of Data
Meaning of data, Classification of data, Methods of collecting data, Methods of presenting data.

003.03 Measures of Central Tendency
Mean, Mode, Median, and Geometric Mean.

003.04 Measures of Dispersion
Range, Percentiles, Deciles, Mean Deviation, Standard Deviation (with property), Variance, Lorenz Curve, Co-efficient of variation (CV), Chebyshev's theorem and Its use.

003.05 Shape of Distribution
Skewness, Moment and Kurtosis.

003.06 Joint Distribution
Simple Correlation and Regression, Error of Prediction.

003.07 Forecasting
Time Series Decomposition method, Exponential Smoothing method, Regression method, and Box-Jankins methods.

Probability –Weight- 15%

003.08 Introduction
Classical approach and relative frequency approach. Multiplication and Addition theorem.

003.09 Discrete Probability Distribution
Uniform distribution, Poisson distribution, and Binomial distribution.

003.10 Continuous Probability Distribution
Normal Distribution with properties.

Statistical Inference –Weight-15%

003.11 Sampling Distributions and Estimation
Population and Samples, Methods of Sampling, Sampling distribution, Point and Interval Estimation.

003.12 Hypothesis Testing
Procedure of Testing Hypothesis, Type I and II Errors, One and Two Tail Test, Test of Hypothesis about population mean, difference between means, Attribute, Proportions, and difference between two proportions.

Text Books
1. Theory and Problems of Mathematical Methods for Business and Economics – Edward T. Dowling 1993.
2  Business Mathematics - D.C. Sancheti and V.K. Kapoor (11th edition)
3. Statistics for Managements- Levin and Rubin (7th edition).
4. Business Statistics - S.P. Gupta and M.P. Gupta (12th edition)
Reference Books
1. Methods of Statistics- M. G. Mostafa
2. Essential of Statistics of Business and Economics–Anderson D.R. (1997 edition).
3. Business Mathematics – An Introduction : Dr. M. A. Taher (3rd edition).
4. Business Mathematics -  Qazi Zameruddin, V.K. Khanna and S.K. Bhambri (3rd edition).
5. Business Mathematics - L.W.T Staffors.
6. Higher Secondary Algebra and Calculus -   A.K.M. Hoque.
7. Basic Statistics for Business and Economics (2nd edition)– Lind D.A. and  Douglas.
8. Elementary Statistics (3rd edition)–Bluman A.G.

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