# F.Y.B.Com: Mathematical and Statistical Techniques

F. Y. B. Com

MATHEMATICAL AND STATISTICAL TECHNIQUES

Unit I

Commission, Brokerage, Discount and Partnership:

Commission and Brokerage : Simple examples on calculation of commission and brokerage.

Discounts : Trade Discount, Cash Discount. Profit and Loss. Sharing of profit in Partnership.

Problems involving mixture of discount and profit are expected.

Unit II

Shares and Mutual Funds:

Concepts of shares, face value, market value, dividend, equity shares preferential shares, bonus shares, Simple examples.

Mutual Funds, Simple problems on calculation of Net Income after considering entry load, dividend, change in Net Asset Value (N.A.V) and exit load. Averaging of price under the ‘Systematic Investment Plan (S.I.P)’

Linear Programming Problems:

Sketching or graphs of (i) linear equation Ax + By + C = 0 (ii) linear inequalities. Mathematical Formulation of Linear Programming Problems upto 2 variables.

Unit III

Introduction

Meaning, Scope and Limitations of Statistics:

Basic Statistical Concepts: Population, Sample, Variable, attribute, parameter, statistic.

Collection of Data:

Primary and Secondary, Sample and Census, Survey (concept only), Tabulation of data upto 3 characteristics (Simple examples)

Diagrams and graphs:

Given a diagram, interpretation of it. Simple bar diagram, Multiple bar diagram, Percentage bar diagram, Pie diagram.

Drawing of frequency curve, frequency polygon, Histogram (class – intervals of equal lengths only) and ogives.

Unit IV

Measures of Central Tendency: Arithmetic mean, Weighted mean, Combined mean, Median , Mode-without grouping, Quartiles (No Example on missing frequency)

Measures of Dispersion: Range, Quartile deviation, Mean deviation from mean Standard deviation and their relative measures. (Concepts of shift of origin and change or scale are not to be done)

Unit V

Elementary Probability Theory:

Concept of Random experiment/trial and possible outcomes; Sample Space and Discrete Sample Space; Events and their types, Algebra of Events, Mutually Exclusive and Exhaustive Events, concept of nCr.

Classical definition of Probability, Addition theorem (without proof);

Independence of Events : P (A ÇB) = P (A) P (B)

Simple examples.

Random Variable: Probability distribution of a discrete random variable; Expectation and Variance; Simple examples.

Concept of Normal distribution and Standard Normal Variate (SNV), simple examples.

Unit VI

Functions Derivatives and Their Applications

Concept of real functions : constant function, linear function, x2, ex, ax, log x, Demand, Supply, Total Revenue, Average Revenue, Total Cost, Average Cost and Profit function. Equilibrium Point.

Derivative as rate measure.

Derivatives of functions : Constant function, xn, ex, ax, log x

Rules of derivatives : Scalar multiplication, sum, difference, product, quotient, simple problems.

Second Order derivatives.

Applications: Marginal Cost, Marginal Revenue, Elasticity of Demand. Maxima and Minima for functions in Economics and Commerce.

Unit VII

Interest and Annuity

Simple Interest and Compound Interest

Interest Compounded more than once a year. Calculations involving upto 4 time periods.

Equated Monthly Instalments (EMI) using reducing & flat interest system. Present value, Future value.

Annuity, Immediate and due : Simple problems with

A = P <img width="72" height="49" src="file:///C:/Users/kalina/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif"/> with n £ 4

Unit VIII

Bivariate Linear Correlation : Scatter Diagram, Computation of Karl Pearson’s Coefficient of Correlation (Case of Bivariate Frequency Table to be excluded), Computation of Spearman’s Rank Correlation Coefficient (case of repeated ranks upto 2 repetition only)

Bivariate Linear Regression : Finding Regression lines by method of least squares.

Properties of Regression Coefficients – i) r = ± <img width="53" height="29" src="file:///C:/Users/kalina/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif"/> ii) (x, y) is a point of intersection of two regression lines.

Unit IX

Times Series : Concept and Components of time series. Estimation of Trend using Moving Average Method & Least Squares Method (only Linear Trend)

Estimation of Seasonal Component using Simple Arithmetic Mean. (For Trend free data only)

Concept of Forecasting using Least Squares Method.

Index Numbers : Concept and uses. Simple and Composite Index Nos. (unweighted, weighted) Laspeyre’s Price Index No., Paasche’s Price Index No. Fisher’s Price Index No., Cost of Living Index No., Real Income, Simple Examples of Wholesale price Index no.

(Examples on missing values should not be done)

Unit X

Decision Theory : Decision making situation; Decision maker, Courses of Action, States of Nature, Pay-off and Pay-off matrix; Decision making under Uncertainty, Maximum, Maximax and Laplace criteria, simple examples to find optimum decision.

Decision making under Risk Expected Monetary Value (EMV)l Decision tree, simple examples based on EMV